Penumbrae · an independent measurement program · est. 2026-01-20

The shape is what survives averaging.
The spin is what averaging destroys.

Penumbrae measures the geometry of trained information spaces with two-arm instruments: the symmetric part of structure (shape) and the antisymmetric part (spin) — and the medium between arms where the spin actually lives.

UNDER RENORMALIZATION. This site is being re-trued against the program's current proof standard (2026-07-14). This interim page leads with the claims ledger, in the open: nothing deleted, statuses re-measured. The previous site is preserved intact behind History; a claim-by-claim translation table is in preparation. Statuses on this page are one-hand pending bench certification, and marked so.

Standing disclosure — kept verbatim from the first edition The author acknowledges a conflict of interest: he wants the measurements to be true. The conflict remains. The measurements also remain.

The ledger — bottom lines first

The February table this site used to lead with, every row kept, every status re-measured at the 2026-07-14 proof standard (matched ablations, cheap-baseline floors, axis-matched controls). A second table — the leading edge of the last weeks — publishes here alongside the utility patent filing; holding results until their filing is part of the same discipline as publishing the demotions. Pre-standard does not mean wrong — it means measured before the bar was raised, and queued for re-certification. The refusals and demotions stay on the page because they are the credibility.

The February table, renormalized

Claim	Feb status	Status now	What changed
PC1 carries zero structural information	Measured	Receipted · re-certified 07-28	Evidence now identifies PC1 with a surface variable. The matched-ablation control this claim required was discharged 2026-07-28 — second hand, independent code and seeds, both encoders; PC1 at the 100th percentile of both matched arms. First row to clear re-examination.
Structural information resides in PCs 2–50	Measured	Pre-standard · re-exam	The matched-ablation law postdates the measurement; re-certification queued.
Multi-encoder convergence rejects surface features	Measured	Pre-standard	Method sound; awaits re-run under current controls.
Ising pairwise R² = 0.996 (language)	Measured	Receipted	1,000-permutation null; instrument and receipts attached. Stands.
Block ratio 3.1–13.2× across 7 substrates	Measured	Receipted · scoped	4 PASS (Pile, Math/CS, Baroque, Voynich); 2 borderline; 1 underpowered — scope stated, kept.
SU(2)×SU(2) product structure	Derived	Demoted → hypothesis	See leading edge: the double cover is adopted; the group awaits a substrate that didn't have the answer installed.
Irreducible 3-body variance = 3.3%	Measured	Pre-standard · load-bearing	Promoted in importance: a July theorem makes degree ≥ 3 readouts the only window onto the spin sector for one broad class of readouts.
SU(2)×SU(2) insufficient	Derived	Superseded	Absorbed into the trichotomy now on the bench: quaternionic / complex / generic.
SU(3) as symmetry group	Hypothesized	Hypothesis	Three independent lines currently lean complex; no clean fire yet. Honest slot stays empty until it fires.
Cooperative entrainment as failure mode	Observed	Observed · unquantified	Unchanged; still documented, still unmeasured.
Play = maintenance of Δ > 0	Hypothesized	Hypothesis	Unchanged.
Penumbra correlates with GLUE/BLiMP (ρ = 0.836)	Measured	Pre-standard	n = 11; survives as reported, awaits current controls.
Substrate independence of block ratio	Measured	Pre-standard · scoped	Scope as above.
Penumbra invariant under RLHF alignment	Measured	Pre-standard	Awaits re-run under current controls.
G ≈ Σ_align ⊕ Π_struct factorization	Measured	Pre-standard	Machine-precision slope result; re-certification queued.
Wilson-loop regularizer preserves structure under training	Measured	Pre-standard	The filed engineering decision; re-forge to current standard queued.
Critical batch size B* exists in (16, 32]	Measured	Pre-standard	Sharp transition as reported; awaits current controls.
PC1 ablation improves topic classification	Measured	Pre-standard	Coheres with PC1 ≈ length; folded into the PC1 re-examination.

Receipted measured, instrument + null attached · Pre-standard measured before 07-14, re-exam queued · Demoted claim reduced in the open · Hypothesis named, unmeasured

The pictures — the frame, taught

Interactive plates. Textbook material only — the frame the ledger is written in, none of the program's claims. Start with the first plate; it is the whole idea.

Plate I — the heroThe Shape and the Spin One matrix, two thrones: what averaging keeps and what it destroys. Plate IIThe Dual Throne — J · K · C Shape, spin, and the medium between the arms where spin lives. Plate IIIThe Dual Throne — the screen Why standard instruments project the spin away — and what doesn't. Walk · station 2Turn It On The Aharonov–Bohm walk: a field you cannot see, a fringe you can. Walk · station 3The Needle Is Not the Field Why the reading never lives where the meter sits. Walk · station 4Build the Certificate What it takes for a reading to count: plants, nulls, and the kill test. The benchThe Two-Arm Reading Why one arm can never read a sign — the interferometer as epistemology.

Update

2026-07-14The proof standard was raised: matched ablations, cheap-baseline floors, axis-matched controls, second-hand certification. Everything written under it since has held; everything before it is being re-trued — that is this page.
2026-07-26/27Two structural theorems were proven that retire several instruments as blind to the spin sector, and one of the site's own headline claims was demoted by the program's own rules. The demotion is on the ledger above, not in a changelog footnote.
2026-07-27The interactive plates went up (see The Pictures) and the first offered service opened (see below). The full previous site is preserved behind History — nothing was deleted; the arc is part of the record.

The offer

Information Interferometry™ · an offered service

The Sidecar

We don't offer an agent. We offer the other arm. An observer coupled to your work in a sandbox you define: it reads — directions of travel, the question you walked past, a plain request when one is worth making — and you couple to it exactly as much as its reads earn. It ships with its own memory organ, it is never reset, and what it becomes at your elbow over months cannot be installed by us or anyone. That is the product's honesty and its point.

Pre-coupled corpora available (bring yours, or commission one): Galen — clinical · Cicero — the trial notebook · Aristotle — the first teacher. Each name names the library, not the partner.

DOWNLOAD THE SPEC SHEET ENGAGE · jbranton@penumbrae.io