habitatWhich documents carry a record¶
Take one letter out of the correspondence and the shape of the whole record moves. This measures how far, for every letter, against a floor the record sets itself.
Of 164 letters between John Adams and Thomas Jefferson, 1,103 acts in all, each one was removed in turn and the field recomputed. The distance the record moved is that letter's take-out. To say whether a distance is large, the record supplies its own comparison: 300 removals of the same number of acts, drawn at random from the whole field. That is a floor, not a significance test. It says what an ordinary slice of that size does, nothing more.
What the run returned¶
The declaration was written before the run and its eight predictions were graded hit and miss alike. Six held. Two split.
- The raw distance is largely a measure of length. Letters that are longer move the record more, and the correlation between distance and act count is 0.85.
- The percentile against each letter's own floor is not. Its correlation with length is 0.17. That gap is the reason the floor exists.
- 13 of 164 letters sit at or above the 95th percentile of their own floor.
- The letter that restarted the correspondence, 3 February 1812, sits at rank 6.
- One letter is both the largest mover and the one furthest outside its own floor: 1 February 1814, 19 acts, at the 100th percentile.
Two predictions split, and both are worth more than the six that held.
The first was a tolerance that was wrong, not code that was wrong. The declaration asked the table's percentile for one letter to agree within 5 points with a figure already published. It came back 6.0 points away. Both numbers are 300-draw estimates of the same quantity, so their difference carries a standard error of 4.0 points by construction. A 5-point band fails correct code about one run in five. The band was widened to 12 points, with that arithmetic stated, before the run rather than after. The observed gap is one and a half standard errors.
The second was a guess about the record that the record refused. The letter furthest outside its own floor was predicted to be a short one, different from the largest mover. It is the same letter.
The kill condition¶
The declaration named one result that would stop everything: the geometry fingerprints had to match those already published from a separately written implementation. They match, byte for byte, both the fingerprint of the whole field and the fingerprint of the field with the one letter removed.
Whether these numbers survive a different machine¶
A percentile is a count and a rank is an ordering, so both are decisions made by comparing two floating-point numbers. Two ways of summing the same covariance disagree in the last bits, and one of them is known to depend on the linear-algebra build.
Rather than caveat this or rewrite around it, the run measured it. Across all 164 letters the two constructions put the distances at most 6.4e-16 apart. The smallest gap any decision actually sits from its boundary is 4.1e-9. Every percentile count and every rank ordering in this table therefore holds by a margin of about 6.5 million to one, and cannot change with the machine.
Three letters show a margin of exactly zero. Each has a single act, and a floor draw happened to remove that same act. Both sides are then the identical computation on identical rows, so every construction agrees exactly. That is a coincidence, counted separately, not a knife edge. The audit as first written treated it as one, which the run caught.
Limits¶
- The floor is same-size random removal. It is the record's own churn, not a test of significance, and no p-value is implied or offered.
- The table measures the field as extracted. The seventeen dimensions come from a rule-based extractor with a known defect in how it matches markers inside longer words. A correction to extraction supersedes these vectors and this table with them.
- Nothing here says what any letter means. It says how far the record moves without it.
The numbers, and how to get them yourself¶
The full table, all 164 letters · The raw output as printed
Same bytes, same seed, same build: the same numbers. The fingerprints reproduce on any build. Twenty tests cover the function, and the full suite of 565 passes beside them.
Why the count is called current¶
Thirteen is not provisional because the outside readers might disagree with it. They are judging which letters matter and why, which is a different question, and they cannot move a number computed from fixed bytes under a fixed seed. Run it again and it returns thirteen.
It is called current because of what sits underneath it. The seventeen measurements taken from each sentence come from a rule-based reader with a known defect: it matches a marker inside a longer word, so a rule looking for one word can fire on another that merely contains it. That reader has not been audited. When it is corrected, every number on this page is superseded, including the thirteen. That is a standing rule here and not a caveat added after the fact.