Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates

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1 Paper I release report — 15 October 2026
2 Komorebi P.
3 
4 Current release
5   Traditional manuscript: 105 pages, 10 main figures,
6   and 22 visual atlas plates.
7   Lean and evidence guide: 44 pages.
8   Machine-native companion: 100 pages.
9   All three current editions share the reviewed 108-record inventory.
10 
11 Formal correspondence
12   All 69 proof-level records are covered at the exact scopes stated in the
13   current correspondence map. No proof-level record remains partial or unmapped.
14   The remaining records are definitions, classical inputs, boundaries or
15   documentary material; they are not counted as additional proved theorems.
16   The formal audit covers 116 formal source modules plus the
17   retained boundary suite. Including that suite, it inventories
18   3513 source-owned entries and checks 3500 logical declarations.
19   3499 declarations pass logical replay; one upstream-name duplicate passes a fresh-name
20   kernel body check after exact type/value comparison. It records 13
21   runtime helpers separately. The full receipt and controls are preserved in
22   formal/evidence/RELEASE_VERIFICATION.json and formal/evidence/whole_closure/.
23   Targeted new semantic reviews cover 47 proof-level records;
24   accepted predecessor correspondences are retained for 22 others. This is
25   not a claim that all 69 records received a fresh independent semantic audit.
26 
27 Computational and publication checks
28   96 exact finite/symbolic visual assertions passed.
29   33 companion tests passed.
30   10 PDF/PNG figure pairs were regenerated and checked.
31   All final PDF pages were rendered and visually inspected. Current source
32   labels, all 108 record destinations, and all delivered copies of each PDF agree.
33   verification/PUBLICATION_QA.json identifies the exact checked PDF hashes.
34 
35 Source and correspondence clarifications
36   The typed grammar uses the standard vertex/arrow presentation of the
37   finite-vertex path algebra; comparison with an arbitrary ideal quotient is
38   explicit. The split-semisimple corollary states compatible decompositions.
39   Primary polynomial factors are monic. Empty and zero seed families and the
40   packet-source upper-bound count are handled explicitly in the source.
41   The relation module is the kernel of seed evaluation, distinguished from
42   the quotient presentation. The machine catalog uses the current text.
43 
44 Evidence boundaries
45   Lean and Mathlib use the pinned compiler and dependency revisions. Upstream
46   cached dependencies are reused. Logical replay uses Lean's official kernel,
47   not an independently implemented checker. Python checks are bounded examples.
48   Noncomputable formal constructions are not advertised as executable solvers.
49   The preserved v1.0.1 runtime has six finite actions and two profile gates;
50   its planner-only entries remain planner-only. Historical receipts keep
51   their original source identity, execution date, and narrower contract scope.
52 
53 Reproduction
54   python3 scripts/build_pdfs.py --check-only
55   python3 scripts/verify_integrity.py
56   Formal reproduction follows formal/evidence/RELEASE_VERIFICATION.json and
57   the included formal build instructions, using the external pinned runtime.

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