Run 04: the Draft 1 receipt gaps and the Draft 2 repairs

Date: 23 September 2026. Scope: receipt closure and bounded access in the direct palindrome paper, with dependency tracing across the other three papers. Current paper editions are unchanged.

Two distinct repairs

The expanded Draft 1 proof of the receipt-rope recurrence says that bridge shadow identifies every receipt in a shared bridge-block tail. The bridge- shadow induction has a strict proper-suffix hypothesis. At the last cell that hypothesis reaches its boundary. Draft 1 therefore used the lemma beyond the case it had proved.

Draft 2 keeps the recurrence but changes the proof. It applies bridge shadow only to all cells except the last, then proves a mirror-prefix lemma showing that both final palindromes have the same required suffix link. This is a substantive proof repair, not a longer explanation of the same argument.

The second gap is representational. Expanded Draft 1 gives an occurrence record one rope root per input letter, but its internal update also needs a pointer to the occurrence record selected by D_c. Existence of a record of that palindrome type does not say how the current state reaches it within a fixed distance. Following suffix links until the matching bridge can take arbitrarily many steps.

Draft 2 adds a typed transition receipt to every direct entry. At the bridge letter it points to the suffix-link record. At every other letter it copies the corresponding receipt from the suffix-link record. Thus the recursive selector is materialized once when the record is created and is later one entry lookup away. The record layout, client step, run invariant, and access inventory all changed to include this field.

Cross-paper effect

The causal paper’s receipt knot uses the repaired endpoint fact as the concrete reason a fresh rope contains a pointer back to its fresh owner. Its Example 9.6 also relies on the companion’s complete bounded client, where the transition receipt is load-bearing. The generic simultaneous-batch compiler, opaque-element staging theorem, and feedback proposition do not depend on the palindrome recurrence. They remain separate from the companion application.

The current causal HTML makes most of this division explicit: it assigns the receipt proof, concrete source implementation, resource certificate, and whole-client normalization to the direct companion. The future aligned causal edition should cite the exact numbered companion edition rather than a moving reading edition.

The real-time multitape transfer paper reaches EPAL through the classical recognizer and does not use the receipt construction. The unary coherence paper studies history transformations rather than the palindrome occurrence- record client. No receipt-repair consequence was found for either paper. This is a dependency statement, not a new certification of those proofs.

Finite evidence

The targeted checker independently verifies:

• 2,934 direct and 1,160 reset mirror-prefix endpoints through half-length 10;
• 8,188 transition-table entries, of which 5,914 are present receipts; and
• an exact bridge-chase family through depth 128, while the stored receipt remains one entry lookup away.

The upstream publication audit records matching endpoint and table counts and larger bridge-shadow/context-tail tests. A full rerun of its long randomized suite was not needed for this bounded comparison. The targeted checker does not verify the concrete persistent sequence implementation, symbolic whole- client normalization, native scaffold neighborhoods, or the final recognizer.

Version-history consequence

The cumulative history for the next aligned direct edition should state both repairs separately:

1. Draft 2 repaired the last-cell proof of the receipt-rope recurrence by adding the mirror-prefix endpoint lemma.
2. Draft 2 changed the record representation by adding direct transition receipts, closing an unbounded-access gap in the internal update.

Calling both changes “expanded exposition” would be inaccurate. Earlier Draft 1 files remain preserved, identified by their hashes in the historical archive. H01 remains active. The next comparison is the later sequence-source, resource-certificate, and whole-client-normalization chain referenced by causal Example 9.6.