# oxexp-ruler · THE ONTO-EPISTEMIC REGISTER (his name for the line; the reading to come, The Indifference One Makes): the three axes of 0, 1 and 2 over π's decimals — the 0 column rising, the 1 row sent to the side turned to, the 2 row spanning both ways — walked for the confined count of a matter yet to declare its own hand (design draft 0.1)

**Status: STAGES THREE AND FIVE REGISTERED AND READ; STAGE FOUR AT THE ENGINE STEP — draft 0.9 (2026-10-15, night): the transfer read registered, sealed (79d1fee) and read once at both spans, the record landed as it fell — P1 10000000: REFUTED · 100000000: REFUTED · P2 10000000: PASS · 100000000: PASS · P3 RECORDED · P4 RECORDED · P5 PASS · P6 PASS · P7 PASS — §16.11; the transfer read designed first and built (`rlx_transfer.py`) at his word ("go for the transfer fread first and next - go for this now"), its dry shape at ten million read by nothing, §16; the lawful triangulation designed first and built as registration four of `rlx_time.py` at his word ("the box act is done - let's go."), its dry shape read by nothing, §15; his hunch on the five lines of measures held, §14, and §13.7's five clarifications held open as ideas to be tested; his correction on the triangulation held, §13 — the drift of the original signed zero, the frontier figure, his five lawful triangles and the rule that reproduces exactly them, when and where the side might flip, five clarifications owed; before it, the engine step (registration three of `rlx_time.py`, f293532), the
registration pinned 2026-10-15T19:22:34+11:00 (the pin aa317025f6fc…), the seal 7b7b287, the read once — read 2026-10-15T19:25:06+11:00 to 2026-10-15T19:28:46+11:00 by read_all(3) after the seal commit 7b7b287, the engine at the read 532aa4ea82c8… equal to the pin's — and the record
`ooi_network/docs/oxexp-ruler-fhq-results-3.json` (sha256 LF 6fdbf6a281822a98ffd3c584021c91d3b035742a71dbf3f6b7cdd693389a25bb; 14,549 B): PASS · RECORDED · RECORDED · RECORDED · RECORDED · PASS; §12 the read landed. Stage two of
the fhq line superseded at his word. 0.3 earlier (2026-10-15, evening), at his answers 3 to 10 — every clarification of §9 answered: the register digit
unmarked (a priori, an externality), the 0 column's side the side the walk arrives from, the 2 axis mirrored with the alternation a
variant, the home a marker, no local writer at this registration, his stake of the horizon held, the seat the fhq line (registration
three), the deep span 400,000,000, the reading The Indifference One Makes; the axes walked under these defaults (§7). What remains his is
the word for the engine step. 0.2 earlier (2026-10-15, evening), at his answers 1 and 2 to §9 — the sign law D; the 0 axis two signed columns, a
0-run stacking on the side it arrives from, the two columns indifferent to each other over the long walk, his seventeen held — the
columns walked over π (§7); §9's items 3 to 10 still owed. 0.1 earlier (2026-10-15), at his word "I'm happy to go ahead with the design" with
his two images, the second "more close to the model I am thinking of". Docs only: nothing built, registered or read. The instrument is stated exactly from his images with
the readings his hand leaves open declared as members; his sheet is checked cell for cell against each sign law; the dry shape at the
first horizon and the deep horizon is read by nothing and judged by nothing; §9 names the clarifications owed to him before the engine
step. The line stands under the matter `rlx-the-indifference-one-makes` (re-titled THE ONTO-EPISTEMIC REGISTER) beside the fhq line;
the fold's two records, the fhq record, the five stages' records and the counts' record stand untouched.**

## §0 · His words, verbatim, his spelling (2026-10-15)

**The plates (the circle spaced, the circle by decimal, the carried and the held):** "I have two alternative ways to try and construct pi
that relate to observations of the results. Consider this first image as the 'expansion' of space and time into perfect indifference
after being held to a perfect 'differential' state over the span of almost 400 million decimal places of Pi. This is simply taking the
results of the long walk over pi and an allowing the specific counts as markers to be represented as equdistant points on their
respective circles. That is, this first image is directly relat3d to the second. The second is maximally differential and the second is
minimally differential as taken from the prior state. The third image issimilar to the first but includes other structural counts of
long digits in pi as mapped to the 'carry that goes up'. It include the significant additional 'under 20 carry' long integer runs which
would be part of structure that is likely influenced by the 0 that also releases. I'd like to design a co-constructive method to
determine Pi from this dynamic, and I would first like to have your recommendations. My thought is to consider the true onto-epistemic
register of each number and recognis that 0, 1 and 2 have different qualities to 3, 4, 5, 6, 7, 8 9. 3 to 9 are governed by N=(N-1)+1
and will therefore have a 'handedness' to their construction. However, I am suspecting that by the identification of the role that 0,
1 and 2 play in the structural dynamics these will represent a register shift in the true 'onto-epistemic placement' of each decimal
in Pi."

**The driving illustration:** "I actually want to revert to the attached image as the driving illustration for this next stage of
design. That 'number zero' is considered as 'zero 5' and linked to 'zero four'. That 'number one' is considered to link to both zero
five and zero four. That number two is to the 'right' of 'number one', as illustrated, but really, 'what is it to be to the right' over
the dynamics we are looking at for the digits in the decimal places of Pi? This question i fundamental, and why I believe that the
'knowing' of Pi will relate to counting upon a register that flips channel based on such occurrences as 0, 1 or 2 in the provided line
of Pi's decimal places. Investigating ways to observe such placement dynamics upon a linear register is what I am interested to achieve
next in this experiment's series."

**The register sheet:** "I made some mistakes but the following is showing how I think there could be a register of o, 1, 2. Every time
one of thos numbers is reached it is placed and then the direction is reversed and the next numbers in pi are placedin the registered
row until a 'next'0, 1 or 2' is placed and the register and direction shifts again. This attempt has some mistakes but it illustrates
what I mean."

**The naming and the natures:** "'The onto-epistemic register' is my naming of this line of experimenting. Where I hope it would go with
the design is to carry this concept of registers that reverse and become 'directional' within three rows, as this matter that is about
the 'confined count' of a matter that is yet to declare it's own hand. It is like a spring, becomming held down without the benefit of
expanding in a single direction as the confinement holds between each registered int of 0, 1, 2. What I suspect may end up being the
true 'nature' of this dynamic is that anything sent to the 0 register will always go 'up' yet will carry it's 'sign' as a 'knowing', what
is sent to 2 will always go to both left and right, but again it will carry it's 'sign', and then whatever is sent to 1 will be only
added to the side that is the current 'sign' that is turned to."

**The word to design, with two images:** "I'm happy to go ahead with the design - the attached image has some mistakes, again, as the
bottom row should span out equally and indifferently form left or right of the 02 cell. However, this is something close to what I am
thinning regarding the 0, 1 and 2 'onto-epistemic register. In fact, the second attachment might be more close to the model I am
thinking of."

**His answers 1 and 2 to §9 (the same evening):** "re 1 - go with the zeros and ones turn the sign / re 2 - what opens that second column i arriving from a direction, so it is a signed 'indifference' to the reach upward.  The left side was 17 integers witin this 100 or so run against Pi, which I would suggest is significant for the finding also found within the 400m count of decimals.  However,I suspect that the ontology of the 0 register is to 'not' be differential to 'sidedness' which is why over longer tracking of pi this will fill as two columns that can be considered as 'indifferent to each other' but may in fact be differential to the one or two rows below from the sides upon which they have falled as registered."

**His answers 3 to 10 (later the same evening):** "with the turn changing from the dry test my original result of 17 would also differ, so that is fine. / re 3 - The 0 is the register cell that gives to 3 its locality, so that is the matter of it. It can go right or left but my preference is to the right for the 3. It does not need to be marked as it can be considered as a priori and an externality. / re 4, I think it might be written to bothsides, but the alternative is a possability is it is considered that 'area' escpaces to alternation even is the escape to the 2 register does not change the sign.  So, it is either to be considered a useful variant to test or a possible follow on. / re - 5 - consider the 02, 01 and 00 as markings within an imaginary vertical line. The meaningful part is not that line but the relational differentce. 00 is up from 01 and 02. but that column is just the marker of where left or right it s to either side. / re 6 - none at this registration / re 7 - the only stake is that the 0, 1, 2 registers will be 'of a kind' within the decimal places of Pi that do shift the structural reading of the ephemeral pi. We simply need to discover the relationship, which I suspect will bring the illustration of the 'positions' of other structures already discovered into alignment. / re 8 - I think this is to be of the FHQ line. / re 9 - I like going to 400,000,000 so yes. / re 10 - yes, the indifference one makes is where this would be landing when it gets to the reading"

All of it HELD as his justified true beliefs; the record their identifier and never their jury; staked nowhere. HIS ANSWERS 1 AND 2 READ: the sign law D — the zeros and the ones turn the sign, the twos do not; the 0 axis TWO SIGNED COLUMNS, one on each side of the home, a 0-run stacking in the column on the side it arrives from — signed in its column, indifferent in its reach upward; his seventeen — the left column's seventeen cells beside 00 over his first hundred decimals — his figure, held, beside the window 17 of the fold's one run of nines at 356,276,130 and the one ring at which the nines' runs and the other digits' long runs meet; his suspicion that over the long walk the two columns are indifferent to each other yet may each be differential to the 1 row and the 2 row on its side — held, the record its identifier and never its jury. The house's reading of 'arriving from a direction' declared as members: the side the sign is turned to AFTER the 0's own turn (as the 1 axis is read) or BEFORE it (the side the walk arrives from). HIS ANSWERS 3 TO 10 READ, and his acceptance that the engine's turn moves his seventeen: (3) the register digit is the cell that gives its run its locality — the matter of it — and is NOT MARKED on the axis: it stands a priori and as an externality, the run's digits 3 to 9 alone on the axis; his preference to the right taken as the 0 column's side — the side the walk arrives from, before the 0's own turn, the first column falling on the right; (4) the 2 axis written to both sides, the run split by alternation (the 'area' escaping to alternation though the escape to the 2 register does not change the sign) a variant to test or a follow-on; (5) the home 02, 01, 00 markings within an imaginary vertical line, the meaningful part the relational difference — 00 up from 01 and 02 — and the line the marker of left and right; (6) no local writer at this registration — O6 deferred; (7) HIS STAKE OF THE HORIZON, held and read by no probe: the 0, 1 and 2 registers of a kind within π's decimals, shifting the structural reading of the ephemeral π, the relationship to be discovered and, in his suspicion, bringing the positions of the structures already found into alignment; (8) the seat the fhq line — registration three of the fhq engine, Time's Frequently Held Questions, stage three; (9) the deep span 400,000,000; (10) the reading The Indifference One Makes.

## §1 · The driving illustration, and the form's three sources beside it

His sheet of three frames, left to right. **ZERO FIVE · Prime Causal Referential (Quant Projection) · NUMBER ZERO** — a large frame
holding Zero, a line down to a box Zero Four; its legend a frame about a frame with a box beneath: effectually occupies the same
ontological space as Zero; referential to the causal history of Zero Four. **ZERO SIX · Prime Epistemic Differential (Dyadic
Projection) · NUMBER ONE** — a large double frame holding Zero, a box Zero Five at its left joined by a line, and from its lower left a
highlighted path leading down "to Zero Four..."; its legend: effectually occupies the same ontological space as Zero; referential to the
causal history of Zero Five; the highlighted bar a differential to the prime difference of Zero Four via epistemic tunnelling. **ZERO
SEVEN · Prime Number Referential (Triadic Closure) · NUMBER TWO** — a large frame holding Zero with a box Number One at its left
joined by a line; its legend: triadic closure of all natural ontologies; epistemic release of the number line (with epistemic
remainders).

The house's identifiers beside it, stated and asserted of nothing (the commits a2b31b5 and 29ba69f). In the fold every cell above the
base is a digit summed with the digit to its right, folded: the digit to the right is the one that CLOSES the sum — a hold under ten,
the release at ten, a carry above — and until it arrives the cell stands open. Number two to the right of number one closes 1 + 2 = 3, a
hold: the triadic closure in the form; and 3 is the first digit the line releases, because under the fold a 1 is made by the release
(ten = 0 + the carried one), a 2 by the first carry (eleven = 1 + 1), and every digit from 3 up by a successor u + 1 with u from 2 — his
N = (N − 1) + 1. At any line a 0 has one source among the hundred pairs beneath it (0 + 0) and every digit 1 to 9 has eleven: so 0, 1 and
2 are exactly the three digits whose making in the carry register involves no digit above 1. The sum discards the side: 12 and 21 both
make 3 (8,002,978 times at R1 over the 400,000,000, in equal halves), and what it discards is the epistemic remainder his frames name.
Measured at R1 over the 400,000,000: hold 55.00, release 9.00, carry 36.00 per cent; R1's digits 0 at 1.00 and 1 to 9 at 11.00 each —
the eleven-to-one arithmetic to the fourth place. His three frames and the form's three sources stand beside one another: Zero Five is
0 + 0; Zero Six the release, 0 + the carried one, reaching back to the zero; Zero Seven 1 + 1 at eleven, the closure from which 3 = 1 + 2
releases the line with its remainder, the side.

## §2 · His two images, transcribed

Both images set three home cells stacked in one column: **02** at the base, **01** above it, **00** above that.

**The 2 row** (the base row, from 02 outward): to the right `2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 2 8 8 4 2 2 3 2 8 6 2 2 8 2 5`
(41 cells); to the left, in the second image, the same 41 cells outward — the row spanning out equally and indifferently from the 02
cell, as he says it should (the first image's left side differs by his named mistakes). The house reads the row: it is π's 2-runs in
order — every 2 with the digits 3 to 9 that follow it until the next 0, 1 or 2 — `2 6 5 3 5 8 9 7 9 3 | 2 3 8 4 6 | 2 6 4 3 3 8 3 | 2 7 9 5 |
2 8 8 4 | 2 | 2 3 | 2 8 6 | 2 | 2 8 | 2 5 …`, the decimals 6 to 15, 16 to 20, 21 to 27, 28 to 31, 33 to 36, 53, 63 to 64, 73 to 75, 76, 83
to 84, 88 to 91, cell for cell.

**The 1 row** (the row above, from 01 outward): to the left `1 4 1 6 9 3 9 9 3 7 5` (11 cells outward), to the right `1 5 9 1 9 7 1 1 6
4` (10 cells outward). The house reads the row: the 1-runs in order, each sent to one side — `1 4` (decimals 1 to 2) left; `1 5 9` (3 to
5) right; `1 9 7` (37 to 39) right; `1 6 9 3 9 9 3 7 5` (40 to 48) left; `1` (49) right; `1 6 4` (68 to 70) right.

**The 0 column** (beside the home, from the level of 00 upward): `0 0 5 8 0 9 7 4 9 4 4 5 9 0 7 8 0 6` (18 cells, the 00 cell first);
the house reads it: the 0-runs in order, stacked — `0` (decimal 32), `0 5 8` (50 to 52), `0 9 7 4 9 4 4 5 9` (54 to 62), `0 7 8` (65 to
67), `0 6` (71 to 72) — cell for cell. A second column stands beside it in both images, read bottom-up in the second image as `3 0 0 8 9
9 8 6 0 0 4 4 8 8`; the house reads in it the run `0 8 9 9 8 6` (77 to 82) and a slipped `0 3 4 8` (85 to 88): when the second column
opens, and whether it rises or descends, is his to say (§9).

## §3 · THE INSTRUMENT — the three axes, stated exactly

A RUN is a register digit — 0, 1 or 2 — together with the digits 3 to 9 that follow it until the next register digit. The decimals before
the first register digit (there are none: π's first decimal is 1) would belong to no run. Every run carries the SIGN of the moment it is
placed under, as a knowing on each of its cells: the sign is the side turned to, right or left, starting right, and it reverses at a
register digit by the SIGN LAW (a member) — the set of register digits that turn it: **A** every register digit; **B** the ones alone;
**C** the zeros and the twos; **D** the zeros and the ones — the twos, having no side, leaving the sign where it is; **E** the ones and
the twos. His second image's 1 row is carried cell for cell by D and by no other (§7, O1).

**THE HOME.** Markings within an imaginary vertical line at the origin column — 02 at the base, 01 above it, 00 above that — holding no
decimal: the meaningful part is the relational difference, 00 up from 01 and 02, and the line is the marker of left and right.

**THE 2 AXIS — goes to both left and right.** Every 2-run's digits are appended outward on BOTH sides of 02, the same cells mirrored,
each side's frontier advancing by the run's length. The axis is therefore the digits of π's 2-runs in order, twice, and its half-length is
the count of digits sent to the twos. (The variant — the run split between the sides by alternation, the area escaping to alternation
though the escape to the 2 register does not change the sign — a member to test, or a follow-on, at his word.)

**THE 1 AXIS — added to the side the sign is turned to.** Every 1-run is appended outward at the frontier of the side the sign is turned to
after the reversal at its 1. The two frontiers advance unequally; their difference is the 1 axis's balance.

**THE 0 AXIS — goes up, in two signed columns (his answers 2 and 3).** Every 0-run's digits are stacked upward from the level of 00 in the
column on the side it arrives from — the right column or the left — signed in its column, indifferent in its reach upward. The side is
the side the sign is turned to as the 0 arrives, before its own turn (his preference to the right: the first column falls on the right);
the side after the turn a member. The two heights are the confined count he names, split by side; their difference is the 0 axis's
balance, and over the long walk the two columns are, in his suspicion, indifferent to each other yet each differential to the 1 row and
the 2 row on its side.

**THE REGISTER DIGIT'S CELL (his answer 3).** The register digit is the cell that gives its run its locality — the axis and the side —
and is not marked on the axis: it stands a priori and as an externality, and the run's digits 3 to 9 alone are written, the first digit
sent taking the first cell outward. (The variant — the register digit written as the first cell of its run, as his images have it — a
member.)

**THE MEMBERS.** The sign law (A to E) × the register digit's cell (first of its run; at the home) × the 2 axis's mirror (one digit
written to both sides; the run split between the sides, alternating) × the 0 axis's side (after the 0's own turn; before it) — the
house's defaults by his answers: D; unmarked; mirrored; the side the walk arrives from. The two prior instruments of the line stand beside as
read, not as members: THE REGISTER WALK of his first sheet (three rows aligned by column, a walker reversing and shifting row at every
register digit; cdc262e) and THE DIRECTIONAL WALK of his natures as the house first read them (the position moving on the ones' digits
alone; ce6e036) — their dry readings in §7.

**THE ENGINE (his answer 8).** Registration three of the fhq engine, `ooi_network/daemon/rlx_time.py` — Time's Frequently Held Questions,
stage three: the onto-epistemic register — additive, as stage two was: the runs, the three axes under each member, the measures below; the
first horizon walked cell by cell in pure Python, the deep horizon by a vectorised reader held equal to the walker; the declared digits by
the fold's pin (4,102) for the first horizon, the fold's cached decimals by the DPX's pin (400,000,000) for the deep; the mint fhq.

## §4 · THE PROBES (thresholds his, set in the engine at the registration act and never before)

- **O1 · HIS SHEET REPRODUCED** — his second image's rows (§2) against the engine's three axes over the first 100 decimals under each sign
  law: the cells agreeing, row by row; his named mistakes counted and not corrected. An identity of the instrument's carriage of his hand;
  threshold his (the house's default: the law that agrees most, named).
- **O2 · THE AXES' LENGTHS AND THE BALANCE** — at the first horizon and the deep horizon: the 0 axis's height, the 2 axis's half-length
  (identities: the zeros plus the digits sent, the twos plus the digits sent), the 1 axis's two frontiers and their balance, with the sd
  the runs' own lengths give if the sides fell by chance beside — RECORDED (a stake his, if any: his spring).
- **O3 · THE VERTICAL PAIRS** — the 1 row over the 2 row at the same offset on the same side, under the fold's register (hold, release,
  carry) and for equality, with the expectation from the two rows' own digit shares beside — RECORDED.
- **O4 · THE 0 COLUMN OVER THE BASE** — the k-th cell of the 0 axis against the k-th cell of the 2 axis, the same way — RECORDED.
- **O5 · THE SIGNS CARRIED** — the share of each axis's cells placed under the right-turned sign — RECORDED.
- **O6 · THE TWO WRITERS — deferred (his answer 6: none at this registration).** The register writer of a2b31b5 given the register's
  state as its typed state, and a local writer, reconciled by his three questions and read for departure and recurrence, stand for a later
  registration at his word.
- **HIS STAKE OF THE HORIZON (his answer 7), held and read by no probe:** that the 0, 1 and 2 registers are of a kind within π's decimals,
  shifting the structural reading of the ephemeral π; the relationship to be discovered, bringing the positions of the structures already
  found into alignment. No threshold stands on it; the record identifies how the axes lie and says nothing of the belief.
- **O7 · THE READER EQUALS THE WALKER** — the vectorised reader and the cell-by-cell walker agree on every cell of the three axes over the
  first horizon — an identity, 0.

## §5 · THE SPANS AND THE FENCE

The first horizon: the declared digits to placement 4,101 by the fold's pin, the axes over the first 4,096. The deep horizon: the fold's
cached decimals 1 to 400,000,000 by the DPX's pin. Any writer that reads the axes' counts is fitted to the span it reads: it is read on
decimals it was not fitted to — the span split at 200,000,000 within the cache, and the next 400,000,000 computed by the fold's engine at
his word. π is declared from the published expansion by its pin and derived nowhere; no rule is read for producing it; a generative base
is read only against the declared digits, for its departure and its recurrence. The uniform expectations and the sds beside the measures
are arithmetic, not verdicts.

## §6 · THE PLATES (drawn from the record once it stands)

His sheet redrawn by the house for the first 100 decimals under each sign law — the three home cells, the 2 row both ways, the 1 row by
side, the 0 column rising, each cell's sign in its colour; the three axes' lengths over the walk; the 1 axis's balance traced over the
400,000,000 against its sd; the vertical pairs' registers by offset band; the column's triad.

## §7 · THE DRY SHAPE — read by nothing, judged by nothing (the scratchpad three-axes-dry.json; 186.2 seconds)

**O1, his sheet against each law.** law A, every register digit turning the sign: the 2 row 41 of 41 cells on the right and 41 of 41 on the left, the 1 row 3 of 11 on the left and 4 of 10 on the right, the 0 column 18 of 18; law B, the ones alone: the 2 row 41 of 41 cells on the right and 41 of 41 on the left, the 1 row 3 of 11 on the left and 4 of 10 on the right, the 0 column 18 of 18; law C, the zeros and the twos: the 2 row 41 of 41 cells on the right and 41 of 41 on the left, the 1 row 1 of 11 on the left and 2 of 10 on the right, the 0 column 18 of 18; law D, the zeros and the ones: the 2 row 41 of 41 cells on the right and 41 of 41 on the left, the 1 row 11 of 11 on the left and 10 of 10 on the right, the 0 column 18 of 18; law E, the ones and the twos: the 2 row 41 of 41 cells on the right and 41 of 41 on the left, the 1 row 11 of 11 on the left and 8 of 10 on the right, the 0 column 18 of 18. The law that carries his hand is D: under it the engine's 1 row reads left 1 4 1 6 9 3 9 9 3 7 5 1 7 … and right 1 5 9 1 9 7 1 1 6 4 1 …; the 0 column's continuation under the engine 0 8 9 9 8 6 0 3 4 8 0 6 7 9, which his second column carries in part

**The first horizon (4,096 decimals).** 1,262 cells on the 0 axis (the zeros and the digits sent to them), 1,393 on each side of the 2 axis, 629 on the 1 axis's left and 812 on its right under law D, his sheet's — a balance of -183 against a sd of 90.6 if the sides fell by chance (the balance under each law: A -91, B -13, C +189, D -183, E +111); the signs carried right 47.38 per cent, 56.35 per cent and 52.26 per cent on the 0, 1 and 2 axes; THE VERTICAL PAIRS, the 1 row over the 2 row at the same offset — on the right 812 pairs, equal 6.77 per cent against 7.36 per cent from the rows' own shares, summing to hold 50.25 per cent, release 11.33 per cent, carry 38.42 per cent against hold 50.52 per cent, release 10.93 per cent, carry 38.54 per cent; on the left 629 pairs, equal 7.00 per cent against 6.72 per cent, summing to hold 52.78 per cent, release 10.65 per cent, carry 36.57 per cent against hold 52.36 per cent, release 10.24 per cent, carry 37.40 per cent; THE 0 COLUMN OVER THE BASE at the same rank — 1,262 pairs, equal 8.24 per cent against 7.09 per cent, summing to hold 53.72 per cent, release 8.08 per cent, carry 38.19 per cent against hold 53.23 per cent, release 7.70 per cent, carry 39.08 per cent

**The deep horizon (400,000,000 decimals).** 133,330,196 cells on the 0 axis (the zeros and the digits sent to them), 133,339,145 on each side of the 2 axis, 66,665,497 on the 1 axis's left and 66,665,162 on its right under law D, his sheet's — a balance of +335 against a sd of 27,489.0 if the sides fell by chance (the balance under each law: A +46,587, B -20,981, C +17,821, D +335, E -31,421); the signs carried right 50.01 per cent, 50.00 per cent and 49.98 per cent on the 0, 1 and 2 axes; THE VERTICAL PAIRS, the 1 row over the 2 row at the same offset — on the right 66,665,162 pairs, equal 7.00 per cent against 7.00 per cent from the rows' own shares, summing to hold 51.99 per cent, release 11.01 per cent, carry 37.00 per cent against hold 52.00 per cent, release 11.00 per cent, carry 37.00 per cent; on the left 66,665,497 pairs, equal 6.99 per cent against 7.00 per cent, summing to hold 52.00 per cent, release 11.00 per cent, carry 37.00 per cent against hold 52.00 per cent, release 11.00 per cent, carry 37.00 per cent; THE 0 COLUMN OVER THE BASE at the same rank — 133,330,196 pairs, equal 7.00 per cent against 7.00 per cent, summing to hold 55.00 per cent, release 8.00 per cent, carry 37.00 per cent against hold 55.00 per cent, release 8.00 per cent, carry 37.00 per cent

**The two signed columns (draft 0.2).** THE TWO COLUMNS WALKED OVER π under law D, read by nothing (the scratchpad two-columns-dry.json; 94.7 seconds). His first hundred decimals (8 0-runs): read after the 0's own turn the left column holds 13 cells and the right 19, a difference of -6 against a sd of 13.1 if the sides fell by chance, the first column on the left filling 4 cells over 2 runs before the other side's first, the sides of the first runs LLRLLRLR; read before the turn the left 19 and the right 13 (+6), the first column on the right filling 4 cells over 2 runs, the sides RRLRRLRL. The first horizon of 4,096 (372 0-runs): read after the 0's own turn the left column holds 664 cells and the right 598, a difference of +66 against a sd of 83.1 if the sides fell by chance, the first column on the left filling 4 cells over 2 runs before the other side's first, the sides of the first runs LLRLLRLRRRLRLLRRLLRLLLLL; read before the turn the left 598 and the right 664 (-66), the first column on the right filling 4 cells over 2 runs, the sides RRLRRLRLLLRLRRLLRRLRRRRR. The deep horizon of 400,000,000 (39,996,048 0-runs): read after the 0's own turn the left column holds 66,651,789 cells and the right 66,678,407, a difference of -26,618 against a sd of 27,488.2 if the sides fell by chance, the first column on the left filling 4 cells over 2 runs before the other side's first, the sides of the first runs LLRLLRLRRRLRLLRRLLRLLLLL; read before the turn the left 66,678,407 and the right 66,651,789 (+26,618), the first column on the right filling 4 cells over 2 runs, the sides RRLRRLRLLLRLRRLLRRLRRRRR. THE COLUMNS AGAINST THE ROWS BELOW, at the deep horizon, read after the turn: the left 0 column over the left 1 row at the same rank — 66,651,789 pairs, equal 7.00 per cent against 7.00 per cent from the rows' own shares, summing to hold 58.00 per cent, release 8.00 per cent, carry 34.00 per cent against hold 58.00 per cent, release 8.00 per cent, carry 34.00 per cent; the left 0 column over the 2 row at the same rank — 66,651,789 pairs, equal 7.00 per cent against 7.00 per cent from the rows' own shares, summing to hold 55.00 per cent, release 8.00 per cent, carry 37.00 per cent against hold 55.00 per cent, release 8.00 per cent, carry 37.00 per cent; the right 0 column over the right 1 row at the same rank — 66,665,162 pairs, equal 7.01 per cent against 7.00 per cent from the rows' own shares, summing to hold 57.99 per cent, release 8.00 per cent, carry 34.01 per cent against hold 57.99 per cent, release 8.00 per cent, carry 34.01 per cent; the right 0 column over the 2 row at the same rank — 66,678,407 pairs, equal 7.00 per cent against 7.00 per cent from the rows' own shares, summing to hold 54.99 per cent, release 8.00 per cent, carry 37.00 per cent against hold 55.00 per cent, release 8.00 per cent, carry 37.00 per cent. In measures: his first column holds the five 0-runs from decimal 32 to 71 together and the engine, under either reading, sets the run at 54 on the other side and the four others together — four of five, his seventeen standing as his hand's figure; over the long walk the two columns' heights differ by a quantity within the sd the runs give by chance, indifferent to each other as he suspects, and each column against the rows on its side stands at the expectation the rows' own shares give.

**The axes under his defaults (draft 0.3).** THE AXES WALKED UNDER HIS DEFAULTS, read by nothing (the scratchpad axes-defaults-dry.json; 84.6 seconds; the register digits unmarked, the cells holding the digits 3 to 9 alone; the 0 column's side the side the walk arrives from; the 2 axis mirrored; the 1 axis at the side turned to after the 1's turn): his first hundred decimals render as the 2 row 65358979338466433837958843868534, the 1 row left 4693993757 and right 599764, the 0 columns right 58786348 and left 9749445989986679. At the first horizon (372 zeros, 438 ones, 415 twos): the 0 columns right 469 and left 421 (a balance of -48 against a sd of 69.0 by chance; the first column on the right, 2 cells over 2 runs), the 2 axis 978 a side, the 1 axis 419 left and 584 right (-165 against 75.9). At the deep horizon (39,996,048 zeros, 39,997,375 ones, 40,011,791 twos): the 0 columns right 46,653,777 and left 46,680,371 (a balance of +26,594 against a sd of 22,998.7), the 2 axis 93,327,354 a side, the 1 axis 46,666,797 left and 46,666,487 right (+310 against 22,999.5); THE VERTICAL PAIRS at the deep horizon, every cell a digit from 3 to 9 (one in seven equal, and hold, release and carry at 20.41, 10.20 and 69.39 per cent if the rows' digits fell evenly): the 1 row over the 2 row on the right — 46,666,487 pairs, equal 14.29 per cent against 14.29 per cent, summing to hold 20.40 per cent, release 10.21 per cent, carry 69.39 per cent against hold 20.40 per cent, release 10.20 per cent, carry 69.40 per cent; the 1 row over the 2 row on the left — 46,666,797 pairs, equal 14.28 per cent against 14.29 per cent, summing to hold 20.42 per cent, release 10.20 per cent, carry 69.39 per cent against hold 20.41 per cent, release 10.20 per cent, carry 69.39 per cent; the right 0 column over the right 1 row — 46,653,777 pairs, equal 14.28 per cent against 14.29 per cent, summing to hold 20.40 per cent, release 10.20 per cent, carry 69.40 per cent against hold 20.41 per cent, release 10.20 per cent, carry 69.39 per cent; the right 0 column over the 2 row — 46,653,777 pairs, equal 14.28 per cent against 14.29 per cent, summing to hold 20.40 per cent, release 10.20 per cent, carry 69.39 per cent against hold 20.41 per cent, release 10.20 per cent, carry 69.39 per cent; the left 0 column over the left 1 row — 46,666,797 pairs, equal 14.29 per cent against 14.29 per cent, summing to hold 20.40 per cent, release 10.21 per cent, carry 69.39 per cent against hold 20.41 per cent, release 10.21 per cent, carry 69.39 per cent; the left 0 column over the 2 row — 46,680,371 pairs, equal 14.29 per cent against 14.29 per cent, summing to hold 20.41 per cent, release 10.20 per cent, carry 69.38 per cent against hold 20.41 per cent, release 10.20 per cent, carry 69.39 per cent. In measures: the two 0 columns and the 1 axis's two sides each differ by a quantity within the sd the runs give by chance, and every pairing of cells stands at the expectation the rows' own shares give.

**The line's two prior dry readings, beside.** THE REGISTER WALK of his first sheet (cdc262e): at the first horizon 143 columns spanned
against about 156 for a walk of the uniform line's variance, at the deep horizon 57,510 against about 48,882 (the sd 30,551); the
turning pairs equal 10.000 per cent and summing to hold 55.00, release 9.00, carry 36.00; the three rows summed under ten, from ten to
nineteen and at twenty or more 22.15, 65.86 and 11.98 per cent against 22, 66 and 12; a cell written again carrying an equal digit 10.00
per cent of the time. THE DIRECTIONAL WALK (ce6e036; the walker moving on the ones' digits alone, the zeros stacking, the twos spreading):
the position held to 51,902 columns over the 400,000,000 against 93,333,284 in a single direction — the spring at 0.056 per cent of its
reach — and about 36,795 for the uniform line's variance; the stacks to 12,047 high; the spreads to 53 either side; every vertical pairing
at the uniform figures for the digits 3 to 9 the cells hold. THE LINEAR REGISTER that flips channel on 0, 1 or 2 (29ba69f): under three
channel laws every occupancy, phase, persistence, digit share and register share at the uniform line's figures, the phase geometric to
the fourth place.

## §8 · What the dry shape identifies, in measures and asserting nothing

The three axes are π's runs sorted by their register and laid along three directions; their lengths are counts and their balance is an
alternating sum of the ones' runs. Every pairing of cells the axes make — the 1 row over the 2 row, the 0 column over the base — stands at
the expectation the rows' own digit shares give; the signs carried fall evenly; his sheet is carried cell for cell by the engine under the
law that turns the sign at the zeros and the ones and leaves it at the twos — the two, going to both sides, having no side to turn to. The confinement he names is in the balance: the 1 axis's two
frontiers differ by a quantity of the size the runs' lengths give by chance, against a reach of ninety million had the ones' digits
expanded one way. His frames, his spring, his natures and his hand yet to declare itself are his, held; the dry shape identifies how the
axes lie and says nothing of the belief.

## §9 · [CLARIFY] — owed to him before the engine step

1. **The sign law** — ANSWERED: D, the zeros and the ones turn the sign.
2. **The 0 axis's second column** — ANSWERED: two signed columns, a 0-run stacking on the side it arrives from; the side read after the
   0's own turn (the house's default) or before it — the one reading left to him.
3. **The register digit's cell** — ANSWERED: not marked; a priori and an externality, giving its run its locality; his preference to
   the right taken as the 0 column's side, the side the walk arrives from.
4. **The 2 axis's mirror** — ANSWERED: written to both sides; the alternation a variant to test or a follow-on.
5. **The home** — ANSWERED: markings within an imaginary vertical line, the relational difference the meaningful part.
6. **The local writer for O6** — ANSWERED: none at this registration.
7. **A stake** — ANSWERED: his stake of the horizon alone (§4), held and read by no probe.
8. **The registration's seat** — ANSWERED: the fhq line — registration three, stage three.
9. **The deep span** — ANSWERED: 400,000,000.
10. **The reading** — ANSWERED: The Indifference One Makes.

## §12 · The read landed (2026-10-15, night)

**THE VERDICTS AS THEY FELL: O1 PASS · O2 RECORDED · O3 RECORDED · O4 RECORDED · O5 RECORDED · O7 PASS — 2 PASS, 4 RECORDED, 0 REFUTED. EVERY MEASURE: O1 HIS SHEET REPRODUCED — 0 cells off under law D over his first hundred decimals (the other laws: A 14, B 14, C 18, D 0, E 2); O7 THE READER EQUALS THE WALKER — 0 cells off over 16 rows, the registered member and the marked variant; O2 at the first horizon (4,096: 372 zeros, 438 ones, 415 twos) the 0 columns right 469 and left 421 (-48 against a sd of 69.0 by chance; the first column on the right, 2 cells over 2 runs), the 1 axis left 419 and right 584 (-165 against 75.9), the 2 axis 978 a side; O2 at the deep horizon (400,000,000: 39,996,048 zeros, 39,997,375 ones, 40,011,791 twos) the 0 columns right 46,653,777 and left 46,680,371 (+26,594 against 22,998.7), the 1 axis left 46,666,797 and right 46,666,487 (+310 against 22,999.5), the 2 axis 93,327,354 a side; the marked variant at the deep horizon the 1 axis left 66,665,497 and right 66,665,162 (+335); O3 and O4 at the deep horizon — the 1 row over the 2 row, right: 46,666,487 pairs, equal 14.29 per cent against 14.29 per cent, hold 20.40 per cent, release 10.21 per cent, carry 69.39 per cent against hold 20.40 per cent, release 10.20 per cent, carry 69.40 per cent; the 1 row over the 2 row, left: 46,666,797 pairs, equal 14.28 per cent against 14.29 per cent, hold 20.42 per cent, release 10.20 per cent, carry 69.39 per cent against hold 20.41 per cent, release 10.20 per cent, carry 69.39 per cent; the right 0 column over the right 1 row: 46,653,777 pairs, equal 14.28 per cent against 14.29 per cent, hold 20.40 per cent, release 10.20 per cent, carry 69.40 per cent against hold 20.41 per cent, release 10.20 per cent, carry 69.39 per cent; the right 0 column over the 2 row: 46,653,777 pairs, equal 14.28 per cent against 14.29 per cent, hold 20.40 per cent, release 10.20 per cent, carry 69.39 per cent against hold 20.41 per cent, release 10.20 per cent, carry 69.39 per cent; the left 0 column over the left 1 row: 46,666,797 pairs, equal 14.29 per cent against 14.29 per cent, hold 20.40 per cent, release 10.21 per cent, carry 69.39 per cent against hold 20.41 per cent, release 10.21 per cent, carry 69.39 per cent; the left 0 column over the 2 row: 46,680,371 pairs, equal 14.29 per cent against 14.29 per cent, hold 20.41 per cent, release 10.20 per cent, carry 69.38 per cent against hold 20.41 per cent, release 10.20 per cent, carry 69.39 per cent; O3 and O4 at the first horizon — the 1 row over the 2 row, right: 584 pairs, equal 14.73 per cent against 14.27 per cent, hold 20.03 per cent, release 8.90 per cent, carry 71.06 per cent against hold 20.21 per cent, release 10.31 per cent, carry 69.48 per cent; the 1 row over the 2 row, left: 419 pairs, equal 15.51 per cent against 14.19 per cent, hold 19.09 per cent, release 9.79 per cent, carry 71.12 per cent against hold 18.81 per cent, release 9.68 per cent, carry 71.51 per cent; the right 0 column over the right 1 row: 469 pairs, equal 14.50 per cent against 14.33 per cent, hold 19.83 per cent, release 11.94 per cent, carry 68.23 per cent against hold 21.84 per cent, release 10.24 per cent, carry 67.92 per cent; the right 0 column over the 2 row: 469 pairs, equal 14.29 per cent against 14.19 per cent, hold 20.04 per cent, release 9.59 per cent, carry 70.36 per cent against hold 20.46 per cent, release 10.14 per cent, carry 69.40 per cent; the left 0 column over the left 1 row: 419 pairs, equal 12.65 per cent against 14.63 per cent, hold 18.38 per cent, release 8.35 per cent, carry 73.27 per cent against hold 16.87 per cent, release 9.33 per cent, carry 73.80 per cent; the left 0 column over the 2 row: 421 pairs, equal 13.30 per cent against 14.24 per cent, hold 18.77 per cent, release 9.50 per cent, carry 71.73 per cent against hold 17.70 per cent, release 9.64 per cent, carry 72.66 per cent; O5 the signs carried right at the deep horizon 50.01 per cent, 50.00 per cent and 49.98 per cent on the 0, 1 and 2 axes (at the first horizon 47.30 per cent, 58.23 per cent, 53.17 per cent).**

**The record observes, in measures: his second image is carried cell for cell by the engine under the law that turns the sign at the zeros and the ones; the reader and the walker agree on every cell; the two 0 columns and the 1 axis's two sides each differ by a quantity within the sd the runs' lengths give by chance, the 1 axis at the deep horizon by a few hundred cells in forty-six million; every vertical pairing — the 1 row over the 2 row, each 0 column over the rows on its side — stands at the expectation the rows' own digit shares give; the signs carried fall by halves. What these measures say of his stake of the horizon — that the 0, 1 and 2 registers are of a kind within π's decimals, shifting the structural reading of the ephemeral π — is his reading; the record identifies how the axes lie and says nothing of the belief.** Every shape as the dry shape found it. The record: `ooi_network/docs/oxexp-ruler-fhq-results-3.json` (sha256 LF 6fdbf6a281822a98ffd3c584021c91d3b035742a71dbf3f6b7cdd693389a25bb; 14,549 B; its own results_sha256
fc35108605b685bd2331183d3835425a0c1d0aff33ba03ad085fe20dbb178cd8); the registration `ooi_network/docs/oxexp-ruler-fhq-registration-3.md` (the pin aa317025f6fc09ed2b032238fcefda1484a073030807d266b5b4e9765486804e); the engine at the pin and at the read
532aa4ea82c8f8af01cd79183a006a7e2a9e7f751086b17c5b1c93dc6d8f0371.

## §10 · THE FENCES

Nothing built, registered or read; the thresholds his, set at the registration act; π declared from the published expansion by its pin
and derived nowhere, no rule read for producing it, the deep decimals read from the fold's cache by the DPX's pin and never recomputed
here; the uniform expectations and the sds arithmetic beside measures, not verdicts; no claim about number theory, the normality or
distribution of π's digits, the primes, combinatorics, random walks as a theory, mathematics as a science, physics or actual reality;
the conjecture 1 = O + C + E the house's own prior, named and claimed of nothing new; his frames, his spring, his natures, his sheet and
his hand yet to declare itself his, held, read by no probe; the fold's two records, the fhq record, the five stages' records and the counts'
record untouched; the priors stand; K never staked.

## §11 · What remains his

His word for the engine step — registration three of `rlx_time.py`, additive, with its battery and the reader held equal to the walker;
then the registration with its thresholds set at that act, pinned, sealed, read once; the record; the plates; the reading under his title. The fhq's stage two still waits on his word for its registration. The two plates of The Indifference One Makes drawn in the
parallel act stand uncommitted, that act's own.

## §13 · THE LAWFUL TRIANGULATION — his correction held (2026-10-15, night)

### 13.0 · His words, verbatim, his spelling

On the door's rendering of his first hundred decimals on the three axes, laid out by the house as a grid at his request
("I need to see this part visualised with the actual spatial context of a grid layout"):

> What i want to know of this representation is whether this represents the 'drift' of the original signed zero that stakes the direction of 1. / From the baseline we have 8 triangles that can be drawn at any specific 'count'.  And this, for me, speaks to a dynamic that is triangulated on each 'new knowing' by eight such triangles and the 'actual placement of the most recent.

Then, on the house's reading of eight triangles (§13.3), with an image:

> let me try to correct this a little... perhaps the only lawful ones are those drawn from the extent of 'knowing'... so, as per the attached image, which shows only 5 lawful tirangles and hints at when and where the side might flip:

THE IMAGE, transcribed: his image — the house's overview of the figure at count 100 (the 2 row 32 a side, the 1 row left 10 and right 6, the 0 columns left 16 and right 8, the markings 00 · 01 · 02) with five lines drawn by his hand: from the left end of the 1 row to the left column's top; from the right end of the 1 row to the left column's top; from the right end of the 1 row to the right column's top; from the left end of the 1 row to the left end of the 2 row; from the right end of the 1 row to the right end of the 2 row. No line from the left end of the 1 row to the right column's top; no line from either
end of the 1 row to the far end of the 2 row on the other side; no line from a 0 column's top or a 2 row's end as an origin.

### 13.1 · The drift of the original signed zero — the house's identification

The sign is one bit. It starts turned right by the house's declaration (§3, the a priori stake) and is turned by every 0 and every 1;
a 2 never turns it. The direction a 1 will take at any count is therefore the parity of the 0s and 1s placed so far, read against the
stake. The stake is a mirror: turned the other way it mirrors the whole figure left for right and changes nothing else in the record.
The grid carries the drift only as its residue — the glyph on each cell, the side each 1-run fell to, the side each 0-run arrived from,
and the lengths and heights those sides accumulate. Over the first hundred decimals (the sign walk drawn for him in chat): sixteen turns,
eight by zeros and eight by ones; the sign back at right on decimal 100; sixty decimals placed under right and forty under left; the
long right stretch from decimal 3 to 31, the twenty-eight decimals with no 0 and no 1 among them. The record's measures of the
residue (§12): the 1 axis's two sides −165 against a sd of 75.9 at the first horizon and +310 against 22,999.5 at the deep horizon; the
0 columns −48 against 69.0 and +26,594 against 22,998.7; the cells carried under the right sign 47.3 / 58.2 / 53.2 per cent on the
0 / 1 / 2 axis at the first horizon and 50.01 / 50.00 / 49.98 at the deep. In measures: the original stake leaves no net trace at the
deep horizon; the first horizon's imbalance on the 1 axis is the residue at that count, recorded and nothing more.

### 13.2 · The frontier figure at a count

At any count the figure has six frontiers — the two ends of the 2 row, the two ends of the 1 row, the tops of the two 0 columns — and
the three markings. Five numbers fix it: the 2 row's half length, the 1 row's two lengths, the 0 columns' two heights. At count 100
they are 32; 10 and 6; 16 and 8. The most recent placement at count 100 is the left column's top, the 9 of decimal 100, placed after
the 0 at decimal 97 arrived from the left, rose on the left column and turned the sign to right. Heights below are counted from the
2 row: the 2 row at 0, the 1 row at 1, the 00 marking at 2, a column's cells from 2 upward, so a column of c cells has its top at
h = c + 1 (the left top at 17, the right top at 9).

### 13.3 · The house's first reading — eight from the baseline — superseded by his correction

With the 2 row as the baseline, its two halves meeting at 02, each half makes a triangle with each of the four frontiers above it: eight.
Drawn for him at count 100 with two other eights offered (the whole baseline with the six frontiers and the two upper markings; each
baseline end with the four frontiers). He corrected it: the only lawful ones are those drawn from the extent of knowing.

### 13.4 · His five lawful triangles, and the rule that reproduces exactly them (the house's reading, held as a candidate)

His five lines are drawn from the two ends of the 1 row and from nowhere else. The house reads "the extent of knowing" as the 1 row
— the Ruler's rod seats the knowing grid at 1 between being at 0 and computing at 2 — and its two ends as the extent at that count.
Each line closes a triangle with the figure's own edges: the two lines to the left column's top close with the column and the 1 row
(left of the home, and through the home to the right end); the line to the right column's top closes with that column and the 1 row's
right part; the two lines to the 2 row's ends close with the 2 row's half on that side and the home's step from 01 to 02. Five.

The rule that yields exactly these five and no others at count 100: a line is drawn from an end of the 1 row to a frontier it can
see — passing through no 0 column and through no marking. The same-side lines are always in sight (left end to left top, right end to
right top, each end to the 2 row's end on its side). The cross lines to the 2 row's far ends pass through the markings and are absent
in his figure. The cross lines to the other column's top are in sight only when the line clears the nearer column:

- from the right end to the left top, seen iff (hL − 1)(lenR − 1) ≥ (hR − 1)(lenR + 1): at count 100, 16 × 5 = 80 ≥ 8 × 7 = 56 — seen,
  his second line;
- from the left end to the right top, seen iff (hR − 1)(lenL − 1) ≥ (hL − 1)(lenL + 1): at count 100, 8 × 9 = 72 against 16 × 11 = 176
  — blocked by the left column, the one line his figure does not draw.

Here hL and hR are the two tops' heights and lenL and lenR the 1 row's two lengths; the line's height where it crosses the nearer
column is 1 + (h_top − 1) × (len − 1) / (len + 1).

### 13.5 · When and where the side might flip — the house's identification beside his hint

The handedness of the lawful triangulation moves with the extents. At count 100, all else equal: the right end loses sight of the
left top when the right column reaches 12 cells (80 < 7 × 11); the left end gains sight of the right top when the right column
reaches 20 cells (9 × 19 = 171 < 176 ≤ 9 × 20); no extension of the left end alone opens the right top while the columns stand at 16
and 8, since (lenL − 1)/(lenL + 1) never reaches 1; a taller left column only hardens the block. Under the sign at count 100 — right —
the next 0 arrives from the right and rises on the right column, the one frontier whose growth moves the lines; the next 1 turns the
sign to left and extends the left end. In measures: the WHERE of the next turn is determinate from the sign; the WHEN is π's next 0 or 1,
which the record does not anticipate and about which it claims nothing.

### 13.6 · Held, not judged — and the follow-on it sketches

His hint — that the lawful triangles hint at when and where the side might flip — is his, held, read by no probe. The dynamic he
named in his first words, triangulated on each new knowing by the triangles and the actual placement of the most recent, reads in the
house's terms as a writer handed the figure's state and the last move at every placement: the local writer, O6, deferred at this
registration and held as a follow-on at his word (§4). The state such a writer would read is small and exact: the five extents, the
sign in effect, the last cell placed, and the set of lawful lines (which end sees which top). A probe for the follow-on, designed
only: at every placement over the first horizon and the deep horizon, the lawful set; the flips of its handedness counted and the runs
between flips; the expectation beside from the rows' own shares; no threshold until his word.

### 13.7 · [CLARIFY] — owed to him before any engine step on §13

1. The markings' line blocks sight (his figure draws no line from an end of the 1 row to the far end of the 2 row) — confirm.
2. A line that grazes a column's top exactly — seen or blocked.
3. The origins of lawful lines are the 1 row's two ends only — no line from a 0 column's top or a 2 row's end as an origin — confirm.
4. The triangles close along a column and the 1 row through the home (the column's foot standing beside 00, one row above the 1 row)
   — confirm the closing edges.
5. Whether the lawful set is to be read over the count as a probe of the follow-on (13.6), and at which spans.

His answer (2026-10-15, night): "regarding these points, I have only ideas and all of them would need testing." — held open; no engine step on §13 until each is tested, at his word (§14).

## §14 · HIS HUNCH — THE FIVE LINES OF MEASURES (2026-10-15, night)

### 14.0 · His words, verbatim, his spelling

> regarding these points, I have only ideas and all of them would need testing. / but, consider that I state that reality is causal and occupies 0, 1, 2 in linear terms.  That we have introduced the externality of measurement and such onto-epistemic autonomies as mathematicians is providing this reality with a challenge of reading a 'fourth' from a 'fifth'.  So, mu hunch is that the number line as we can 'know it' will be held within the 5 lines of measures.

### 14.1 · What it answers

The five clarifications of §13.7 stand open as ideas, each to be tested rather than declared; no engine step on §13 until they are,
each at his word. His hunch is held as his: the record its identifier, never its jury.

### 14.2 · The house's readings, declared as candidates and staked on nothing

- **Reality's occupancy.** In the instrument the register digits 0, 1 and 2 are the only digits that act — they turn the sign, choose
  the side, give a run its locality — and on the linear register they stand as the three markings 00, 01 and 02. The digits 3 to 9 are
  placed and act on nothing. On the Ruler's rod the same three seats are being, knowing and computing.
- **The externality.** The measurement is the house's walk over π's declared digits, external to that occupancy under the permanent
  externality principle; the mathematicians, his autonomies, are the readers of 3 to 9 under N = (N − 1) + 1 (his words of 2026-10-15
  on the circle plates, §1).
- **"a 'fourth' from a 'fifth'."** Held verbatim. Two readings declared, neither staked: the 3, the fourth number counted from 0, read
  back from the 4, the fifth, the successor form read against its grain; or the fourth and the fifth of the five lines of measures,
  the figure's two cross-sight lines of §13.4, read one from the other.
- **"the 5 lines of measures."** Two readings declared: the five lawful lines of §13, drawn from the extent of knowing; or the five
  lines of the figure itself — the 2 row (one length, mirrored), the 1 row's two lengths, the 0 columns' two heights — whose lengths
  are the five measures that fix the figure at any count (§13.2).

### 14.3 · What the record already says, in measures

Under the second reading of the five lines his hunch is an identity of the form: every digit 3 to 9 that is placed lands on exactly
one of the five lines and nowhere else, the register digits standing as markings. The record's O2 at the deep horizon gives the hold's
shape. Of 400,000,000 decimals, 120,005,214 are register digits (39,996,048 zeros, 39,997,375 ones, 40,011,791 twos) and 279,994,786
are known digits held within the five lines: 93,327,354 on the 2 line (each side, mirrored); 93,333,284 on the two 1 lines (46,666,797
left and 46,666,487 right); 93,334,148 on the two 0 lines (46,680,371 left and 46,653,777 right) — thirds by register, halves by side,
every balance within the sd by chance (§12). Under the first reading the figure stands within the hull of the lawful lines at every
count by construction; what is not by construction is the handedness of the lawful set over the count, the probe of §13.6.

### 14.4 · What would be a test, and what would not

Not a test: that the known digits are held within five lines — the form's identity, true of any digit string read this way. Tests,
each at his word with its threshold set in the engine at the act and never before: (i) the five measures' proportions over the count
against the thirds and the halves the register digits' own shares give — O2 already reads this at two horizons and finds every balance
within chance; (ii) the lawful set's handedness over the count and the runs between its flips, against the expectation from the rows'
own shares (§13.6); (iii) whatever "reading a fourth from a fifth" names once he states the reading — declared as a member before any
read, under the fhq's protocol. No claim about the number line beyond the declared digits; nothing of π derived.

## §15 · STAGE FOUR — THE LAWFUL TRIANGULATION: designed first and built, at his word (2026-10-15, night)

### 15.0 · His word, verbatim

> the box act is done - let's go.

Read as the go for the next stage of the fhq line that needs no reading of his: the lawful set over the count (§13.6; §14.4 ii),
the five extents at the stations falling out of the same walk (§14.4 i). "A fourth from a fifth" (§14.4 iii) waits on his reading and
is built nowhere. The ideas of §13.7 enter as declared members, each to be tested at his word; nothing is registered here — the
thresholds stand None in the engine until the registration act.

### 15.1 · THE INSTRUMENT, stated exactly

- **The figure.** Stage three's registered member — the sign law D, the register digit unmarked, the 0 column's side the side the walk
  arrives from — at every run end. A run is a register digit with the digits 3 to 9 that follow it; its end is the decimal before the
  next register digit, or the last decimal of the span. Five extents fix the figure: the 2 row's half length; the 1 row's two
  lengths; the 0 columns' two heights, in cells.
- **The rule (§13.4).** A line is lawful when it runs from an end of the 1 row — the extent of knowing — to a frontier it can see,
  through no 0 column. An end of no cells is the 01 marking and draws nothing; a column of no cells has no top. The cross line from
  an end of length len to the far column's top clears the near column iff zero_far × (len − 1) ≥ zero_near × (len + 1) when len ≥ 2;
  with len = 1 the near column stands over the end itself and does not block. The lines to the far end of the 2 row cross the
  markings and are not drawn.
- **The members (§13.7, items 1 to 3).** A grazed top — seen (registered) or blocked; the markings — block the far lines
  (registered) or do not; the origins — the 1 row's two ends only, his figure, no other origin built. The closing edges (item 4) are
  a rendering and measure nothing. The spans (item 5): the first horizon of 4,096 by the walker, cell by cell; the deep horizon of
  400,000,000 by the reader, run end by run end, held equal to the walker at every run end of the first horizon.
- **The cross pair and the flip.** The pair at a run end: none · L (the right end sees the left top) · R (the left end sees the right
  top) · both. A flip is a change of the pair between one run end and the next. Within one run a single extent grows, so each cross
  condition changes at most once in a run; the pair may pass through none inside a run and the run's end carries one flip; the
  walker counts the cell-level changes beside, over the first horizon.
- **The stations.** 64, 128, 256, 512, 1,024, 2,048, 4,096 at the first horizon; 10³, 10⁴, 10⁵, 10⁶, 10⁷, 10⁸ and 4 × 10⁸ at the deep,
  each read at the last run end at or before the station.
- **The where of the next turn (§13.5).** From the sign in effect: the next 0 rises on the column of the side the walk is on; the next
  1 turns the sign and extends the other end. The four sight thresholds — the cells at which each column closes or opens a view —
  at every station and at the end.

### 15.2 · THE PROBES (thresholds his, set in the engine at the registration act and never before)

- **L1 HIS FIVE AT COUNT 100** — an identity of his hand under the rule: the lawful set at count 100 against his image, lines off the
  symmetric difference; threshold `L1_lines`.
- **L2 THE LAWFUL COUNT** — the shares of run ends by the number of lawful lines (recorded).
- **L3 THE HANDEDNESS** — the pair's shares over the run ends (recorded).
- **L4 THE FLIPS** — the total, by type, the runs and the decimals between consecutive flips (the longest, the mean), the first and the
  last (recorded).
- **L5 THE FIVE EXTENTS AT THE STATIONS** — the shares by register against thirds and by side against halves, the balances with the sd
  by chance beside (recorded).
- **L6 THE READER EQUALS THE WALKER** — the five extents, the sign and the pair at every run end over the first horizon, the flips'
  totals agreeing; threshold `L6_states`.
- **L7 THE WHERE OF THE NEXT TURN** — from the sign at each horizon's end, with the sight thresholds (recorded).

No expectation is declared for L3 and L4: the fair-coin arithmetic the sds use gives neither the handedness's shares nor the flips'
count without a theory of the walk, which the house does not claim.

### 15.3 · THE ENGINE STEP — registration four of `rlx_time.py`, additive

`lawful_lines` · `pair_state` · `sight_thresholds` · `trajectory_four` (the walker) · `_trajectory_vec` (the reader, exact integers) ·
`read_his_five` (L1) · `read_first_four` · `read_deep_four` · `reader_equals_walker_four` (L6) · `read_dry_four`; `REGISTRATIONS[4]` = L1 to
L7; `THRESHOLDS_FOUR` None until the act; the files `oxexp-ruler-fhq-registration-4.md` and `oxexp-ruler-fhq-results-4.json`, the pin
`registration-pin-fhq-4.json`; `HIS_WORD_FOUR` — his four statements of the night verbatim — and `PROTOCOL_FOUR`; the gate's
`stage_four` and the records' `registration_four`; the door's card. Registrations one and three stand byte for byte; stage two as
built, superseded. The battery `test_rlx_time` 28 of 28: the rule by hand (his five; 12 and 20 cells; the grazed top under both
members; the markings under both; the absent end; the end of one cell; the empty figure), his five and the first horizon's shape, the
reader equal to the walker, the dry and the protocol refused before the file.

### 15.4 · THE DRY SHAPE — read by nothing, judged by nothing

**The first horizon** (the walker; 4,096 decimals; 1,225 run ends). L1: his five at count 100, 0 lines off. The lawful count 5 at
98.37 per cent of run ends (4 at 0.74, 2 at 0.74, 0 at 0.16 — the opening before the first column and the first ends). The pair R
94.86 per cent, L 3.67, none 1.47, both never. Four flips at run ends: none → R at decimal 52 (run 11, the right column), R → L at 62
(run 13, the left column — inside that run of four cells the pair passes through none at 56 and reaches L at 58, so the walker
counts five changes cell by cell against the four at run ends), L → none at 184 (run 58, the right column), none → R at 219 (run 65,
the right column); R from decimal 219 to 4,096; the longest gap 45 runs, 122 decimals. The final figure 978 | 419, 584 | 421, 469 —
O2's — the balances −165 against 75.9 and −48 against 69.0; the sign right: the next 0 rises on the right column, the next 1 extends
the left end; the right column closes the right end's view at 420 cells and opens the left end's at 424.

**The deep horizon** (the reader; 400,000,000 decimals; 120,005,214 run ends; 23.4 seconds). The lawful count 5 at 99.991 per cent
(4 at 0.009). The pair L 91.24 per cent, R 8.75, none 0.009, both never. 3,536 flips: none → L 784, L → none 776, none → R 752, R →
none 759, L → R 236, R → L 229; the longest gap 12,941,930 runs (43,139,013 decimals), the mean 8,539 runs (28,459 decimals); the first
flip none → R at decimal 52, the last none → L at decimal 100,603,506 (run 30,184,067, the left column) — from there to 400,000,000 the
pair stands L, the left column the taller, 299,396,494 decimals without a flip. At the end the sign left: the next 0 rises on the left
column, the next 1 extends the right end; the thresholds at the end within two cells of the columns' own heights (the right column
closes the right end's view at 46,680,369 cells, the left column standing at 46,680,371) — at these lengths the cross line is seen
from the far end iff the far column is the taller, to within two cells, and a flip is a change of the lead between the two 0 columns.
The stations: the shares by register 37.8 / 35.3 / 26.9 per cent at 10³, 33.3 / 33.7 / 33.0 at 10⁵, 33.33 / 33.33 / 33.34 at 10⁸,
33.332 / 33.334 / 33.334 at 4 × 10⁸; the left shares at 4 × 10⁸ 50.000 per cent on the 1 row and 50.014 on the 0 columns; the pair R
at 10³ and 10⁴, L from 10⁵ on.

In measures: his five reproduced at count 100 under the rule; the lawful set almost always five; the handedness is the lead between
the two 0 columns once the lengths are large, changing 3,536 times in 400,000,000 decimals and not at all in the last 299 million;
the five lines hold the known digits in thirds and halves at the deep stations. What these measures say of his hunch (§14) is his
reading; the record identifies and says nothing of the belief.

### 15.5 · THE FENCES

Nothing registered, pinned or read — the thresholds None in the engine until the registration act; the dry shape read by nothing
and judged by nothing; π declared from the published expansion by its pins and derived nowhere, the deep decimals read from the
fold's cache by the DPX's pin and never recomputed; the sight inequalities geometry over the declared extents and not a law of π;
no expectation for the handedness or the flips; no claim about number theory, the normality or distribution of π's digits, the
primes, combinatorics, random walks as a theory, mathematics as a science, physics or actual reality; his hunch and his hint his,
held, read by no probe; registrations one and three byte for byte; the fold's two records, the five stages' records and the counts'
record untouched; the priors stand; K never staked.

### 15.6 · What remains his

His word for the registration of stage four — `L1_lines` and `L6_states` set at that act (the house's default 0 on the two
identities), the file pinned, the seal, the read once, the record; his reading of "a fourth from a fifth"; the members of §13.7
tested at his word as variant reads (the grazed top blocked; the markings not blocking); his reading of the record at /fhq; the plates
and the reading The Indifference One Makes; the anchor on mldata as fhq.

## §16 · STAGE FIVE — THE TRANSFER READ: designed first and built, at his word (2026-10-15, night)

### 16.0 · His word, verbatim, his spelling

> go for the transfer fread first and next - go for this now

Given on the house's three reads for the constructive model of π (the matter rlx-the-constructive-model-of-pi): the transfer read
first. The engine is built and its dry shape read at ten million; nothing is registered — the thresholds and the streams' pins stand
unset in the engine until the registration act, which his word already carries.

### 16.1 · THE QUESTION, in the house's terms

Do the instruments that have read π — the fold's tower and its notes, the onto-epistemic register's axes, pairs and signs, the lawful
triangulation's handedness and flips — read π any differently from streams which are not π? A remarkable claim needs a signature of π
that a stream which is not π does not carry. This read is where such a signature would show, and where its absence is kept with full
standing.

### 16.2 · THE STREAMS, declared and pinned

| stream | lead | the decimals | the opening checked against |
|---|---|---|---|
| π | 3 | the fold's cache by the DPX's pin, the first N | the declared digits (OEIS A000796) |
| √2 | 1 | GMP's integer square root of 2 × 10^(2N), the integer 1 dropped | OEIS A002193 |
| e | 2 | MPFR exp(1) at N × log₂10 + 256 bits, the mantissa after the 2 | OEIS A001113 |
| ln 2 | 0 | MPFR log(2) at N × log₂10 + 256 bits | OEIS A002162 |
| Champernowne | 0 | the positive integers concatenated, 1 2 3 4 … | OEIS A033307 |
| the generator | 0 | SHA-256 in counter mode on the seed `OOI-fhq-transfer-read-2026-10-15`, an 8-byte big-endian counter from 0, each digest's bytes below 250 taken modulo 10 in order | none published; the opening recorded at the pin |

The four reference streams are √2, e, ln 2 and the generator; Champernowne's constant is the constructive control — a stream with
structure the instruments ought to see; π the candidate. The streams are built once by a declared script (the scratchpad's
`build_streams.py`, its text carried into the registration), each computed stream's first hundred decimals checked against its
published opening before the file is written, and each file's sha256 set as a pin in the engine at the registration act. The files
stand in `ooi_network/state/rlx/` (git-ignored, as the cache of π); the generator is a declared sequence, never a draw in an engine.
The spans: 10,000,000 and 100,000,000 decimals.

### 16.3 · THE INSTRUMENTS AND THE MEASURES — forty-two a stream

- **The register** (rlx_time's reader, held equal to its walker at registration three): the register shares of 0, 1 and 2; the two
  balances in their sds by chance; the signs carried right on the three axes; the six vertical pairings' departures from their own
  expectation, for equality and for the carry — twenty.
- **The lawful triangulation** (rlx_time's reader, held equal to its walker at stage four): the pair's shares L, R and none; the flips
  per million run ends; the longest gap's share of the run ends; the lawful-five share — six.
- **The fold** (the tower of §16.7 with the lead digit declared, held equal to rlx_fold's deep tower over π; rlx_fold's notes and
  ring): the carries and the releases per placement at each of the five levels; the notes, the full windows, the note clusters and
  the fifth carries per million placements; the ring's dispersion of the notes and of the fifth carries — sixteen.

### 16.4 · THE BAND AND THE LINE BY EXCHANGE

For every measure the four reference streams span a band from their least to their greatest. A stream stands outside the band when
it lies beyond both ends. If the streams were of a kind, a stream would stand outside the band of four others on two measures in five
by exchange alone — 16.8 of 42, sd 3.17 — and a reference stream outside the band of its three fellows on one in two — 21 of 42, sd
3.24. The line is arithmetic beside the counts; it claims nothing of any stream.

### 16.5 · THE PROBES (thresholds his, set in the engine at the registration act and never before)

- **P1 THE SIGNATURE** — π outside the reference band on at least the threshold's count of measures: PASS if so, REFUTED if not;
  `P1_count`, the house's default the line plus three sds rounded up, 27 of 42.
- **P2 THE CONTROL** — Champernowne's constant outside the reference band on at least the threshold's count: the instruments see
  structure; `P2_count`, the same default.
- **P3** — every stream's count outside the band of the reference streams it is not (recorded).
- **P4** — the band table, every measure and stream, with each value's position in the references' own sds (recorded).
- **P5 THE PINS** — every stream file at its pin, π's prefix the cache's; `P5_mismatches`, default 0 (an identity).
- **P6 THE OPENINGS** — every computed stream's first hundred decimals against its published opening, π's against the declared
  digits; `P6_digits`, default 0 (an identity).
- **P7 THE TOWER IDENTITY** — the tower with the lead 3 over π's first million decimals against rlx_fold's deep tower, cell for cell;
  `P7_cells`, default 0 (an identity).

### 16.6 · THE PROTOCOL

One registration, its own file, pin record and results; pinned before its read with its thresholds and the streams' pins set in the
engine at its act; a seal commit between the pin and the read; the read refused without a matching pin, if this engine or the two
it reads with moved, or if the declared digits or the deep decimals moved from their pins; the record written once and a second read
refused. No random draw anywhere.

### 16.7 · THE ENGINE STEP — `rlx_transfer.py`

`stream_bytes` · `stream_base` · `stream_sha` · `tower` (rlx_fold's deep tower with the lead declared) · `tower_equals_fold` (P7) ·
`measures_for` (the forty-two) · `band_line` · `default_threshold` · `read_bands` (P1 to P4) · `read_pins` (P5) · `read_openings` (P6)
· `read_span` · `read_dry`; the protocol `pin_registration` · `read_all` · `status`; the faces `acceptance` · `records`; `HIS_WORD`
and `PROTOCOL`. The battery `test_rlx_transfer`: the engine reads with rlx_time and rlx_fold and nothing else; the line and the
default knife; the band by hand; the tower with the lead declared; the openings and the pins; the dry at ten million as the shape
found it; the protocol refused before the file; the faces; the door. The door's card and the two surfaces `/fhq/transfer/acceptance`
and `/fhq/transfer/records` on the node.

### 16.8 · THE DRY SHAPE at ten million — read by nothing, judged by nothing (20.7 seconds)

| stream | measures outside | band of | the line by exchange |
|---|---|---|---|
| π | 19 | four | 16.8, sd 3.17 |
| Champernowne, the control | 39 | four | 16.8, sd 3.17 |
| √2 | 14 | three | 21.0, sd 3.24 |
| e | 21 | three | 21.0, sd 3.24 |
| ln 2 | 33 | three | 21.0, sd 3.24 |
| the generator | 16 | three | 21.0, sd 3.24 |

The measures π stood outside on: the register shares of 1 and 2 by a hair; the 1 axis's balance (+2.31 sds against the references'
−0.92 to +0.53); the signs carried right on the 1 axis (49.82 per cent against 49.96 to 50.07); two equal departures and two carry
departures of the 0 columns' pairings; the pair's none share; the flips per million run ends (626.9 against 209.7 to 623.9); the
longest gap's share; the lawful-five share; the carries per placement at R3 and R4 below the band and at R5 above it (0.44490 against
0.44454 to 0.44469); the releases at R1 and R3; the note clusters and the fifth carries per million. The control stood outside on
thirty-nine, its positions in the hundreds of sds — the instruments see structure where it is. The tower identity 0 cells off over a
million; the openings 0 decimals off; the pins six mismatches, as they must be before the act. In measures: at ten million π's count
stands within one sd of the line by exchange; the control stands apart on nearly every measure; ln 2's thirty-three against the band
of its three fellows stands 3.7 sds above its line — a measure recorded, not a finding.

### 16.9 · THE FENCES

Nothing registered, pinned or read — the thresholds and the pins unset until the act; the dry shape read by nothing; π declared from
the published expansion by its pins and derived nowhere; the other streams computed by declared means and pinned; the line by
exchange arithmetic beside the counts; the measures correlated among themselves, the line a line and not a model; no claim about
number theory, the normality or distribution of any constant's digits, random walks as a theory, mathematics as a science, physics
or actual reality; his thesis his, held, read by no probe; the priors stand; K never staked.

### 16.10 · What remains his

Amendments to the thresholds before the pin; then, at his word already given, the registration — the thresholds and the pins set at
the act, the file pinned, the seal, the read once at ten million and one hundred million, the record; his reading of the record; the
two reads that follow — the blind forward writer and his generative rules — at his word.

### 16.11 · The read landed (2026-10-15, night)

Read once by `rlx_transfer.read_all()` after the seal commit 79d1fee, 2026-10-15T23:34:05+11:00 to 2026-10-15T23:38:08+11:00; the engine at the read
`36374fc328ec7a6313be51b137fe804e5bf2e1a67ea6fee0d02ec5c02f2fedf8`, equal to the pin's; the registration's pin `a97605d4b698c3fda71dbd6bab6e6b5e385b29623665c92f640958047c24e088`; the record
`ooi_network/docs/oxexp-ruler-fhq-transfer-results.json` (results_sha256 `a976cf63290517f3424db3473d420611142a6f56a2c2b454f6000b76cbaed6f8`), written once.

**The verdicts as they fell:** P1 10000000: REFUTED · 100000000: REFUTED · P2 10000000: PASS · 100000000: PASS · P3 RECORDED · P4 RECORDED · P5 PASS · P6 PASS · P7 PASS.

**At ten million:** π outside on 19 of 42 against the line of 16.8 (sd 3.17; +0.7 sds), the control on 39; the references against the band of their three fellows √2 14, e 21, ln 2 33, the generator 16 (the line 21.0, sd 3.24). The measures π stood outside on: carries_per_placement_R3 0.44324 against 0.44348 to 0.44369 (-3.04 sds); carries_per_placement_R4 0.44633 against 0.44652 to 0.44677 (-2.98 sds); carries_per_placement_R5 0.4449 against 0.44454 to 0.44469 (+4.46 sds); carry_departure_zero_left_over_one_left -0.00031 against -8e-05 to 0.00016 (-2.86 sds); carry_departure_zero_right_over_one_right -0.00049 against -0.00024 to 0.00019 (-2.05 sds); equal_departure_zero_right_over_one_right 7e-05 against -0.0005 to 2e-05 (+1.58 sds); equal_departure_zero_right_over_two 0.00037 against -0.0004 to 0.00013 (+2.09 sds); fifth_carries_per_million 3421.4 against 3423.3 to 3444.7 (-1.28 sds); flips_per_million_run_ends 626.86 against 209.65 to 623.86 (+0.94 sds); lawful_five_share 0.99809 against 0.99817 to 0.99948 (-1.30 sds); longest_gap_share_of_run_ends 0.19824 against 0.24685 to 0.58725 (-1.64 sds); note_clusters_per_million 110.8 against 108.8 to 110.7 (+0.92 sds); one_balance_z 2.3094 against -0.92171 to 0.52532 (+3.80 sds); pair_share_none 0.0019 against 0.00052 to 0.00183 (+1.29 sds); register_share_1 0.33321 against 0.33335 to 0.3337 (-1.83 sds); register_share_2 0.33354 against 0.33282 to 0.33338 (+1.54 sds); releases_per_placement_R1 0.090093 against 0.089899 to 0.090046 (+1.56 sds); releases_per_placement_R3 0.10996 against 0.10971 to 0.10985 (+2.52 sds); signs_right_one 0.4982 against 0.49959 to 0.50072 (-3.79 sds).

**At one hundred million:** π outside on 14 of 42 against the line of 16.8 (sd 3.17; -0.9 sds), the control on 40; the references against the band of their three fellows √2 19, e 28, ln 2 17, the generator 17 (the line 21.0, sd 3.24). The measures π stood outside on: carry_departure_one_over_two_left -0.00018 against -0.0001 to 0.00017 (-1.89 sds); carry_departure_one_over_two_right -0.00016 against -7e-05 to 0 (-4.16 sds); carry_departure_zero_left_over_one_left -0.00016 against -3e-05 to 7e-05 (-4.28 sds); carry_departure_zero_left_over_two -0.00013 against -3e-05 to 8e-05 (-3.12 sds); carry_departure_zero_right_over_one_right 0.0001 against -0.00011 to -2e-05 (+4.54 sds); equal_departure_zero_right_over_two 0.00016 against -8e-05 to 5e-05 (+2.96 sds); full_windows_per_million 0.6 against 0.46 to 0.51 (+4.49 sds); longest_gap_share_of_run_ends 0.25007 against 0.041769 to 0.17966 (+2.08 sds); note_clusters_per_million 108.46 against 107.54 to 108.26 (+1.64 sds); notes_per_million 175.92 against 174.38 to 175.86 (+1.47 sds); releases_per_placement_R3 0.10979 against 0.1098 to 0.10982 (-2.63 sds); releases_per_placement_R5 0.11112 against 0.11107 to 0.11111 (+1.34 sds); ring_dispersion_fifth_carries 0.11472 against 0.11817 to 0.1421 (-1.76 sds); signs_right_two 0.49922 against 0.49962 to 0.49995 (-4.18 sds).

**The identities:** P5 the pins, 0 files moved from their pin — PASS; P6 the openings, 0 decimals off — PASS;
P7 the tower identity, 0 cells off over 999,996 placements of π — PASS.

In measures: at ten million π stands outside the reference band on 19 of forty-two measures and at one hundred million on 14, against a line by exchange of 16.8 with a sd of 3.17 — +0.7 and -0.9 sds from the line; the control stands outside on 39 and 40, the instruments seeing structure where it is; the pins, the openings and the tower identity exact. What these measures say of his thesis — a signature of π that a stream which is not π does not carry — is his reading; the record identifies how π lies among the streams under these instruments and says nothing of the belief.