Contiguous research campaign · C23–C52 · 30 numbered records

Extended 529 Mirror graph and endpoint atlas

Develops a compact coordinate model and extends the admitted endpoint graph through 15/19/22/24-fold families while preserving phase, source-state, canonical-reflection and local-complement distinctions.

Part of the C23–C52 broader study sequence: Extended 529 Mirror graph and endpoint atlas.

Campaign manifest (JSON) · Complete numbered records · All research sections

Related subjects: Mirror & 529

Reading route for researchers and AI readers

Read the current explanation, then select the topic matching your question. A topic may join several separate research campaigns.
Read the selected Start here documents before opening a complete numbered-record list. Follow their cited source editions and evidence links as needed.
Use a campaign for one contiguous line of study; use a topic to find related work revisited across campaigns. The topic and campaign JSON lists contain links and edition hashes, not document bodies.
Original numbered records retain their historical scope and source assumptions. Later corrections, accepted source decisions and the current synthesis govern the present account.
If a subject is absent from the published Knowledge Catalog, consult Study documents and the source guide for supporting studies used or referenced in the C-series research.

Current explanation · Current Strategy review · Source guide and supporting studies · Source guide (Markdown) · Full source catalog (JSON)

Start here: selected leads

C52 — Thirty-step Mirror synthesis: where 6877 belongsResearch action · 490d_C52_Mirror_Report_20260922.md
SHA-256 1d8418b2070995e686a5e4dad6301fe0fa0b28f235f1fc504b47b375df9bf484Download preserved edition · Document JSON
C50 — Endpoint atlas for the full 6877 constructionsResearch action · 490d_C50_Mirror_Report_20260922.md
SHA-256 6d4b13bf9e8a07fc16a13c07497b4a8cda6bf1e6a5d146b175dc00cb8223ac05Download preserved edition · Document JSON
C43 — The extended typed graph has eleven selected family labelsResearch action · 490d_C43_Mirror_Report_20260922.md
SHA-256 e3b3e4582a306149b2af4aaa161d119ef53c24780e4a9b8850e608d8c680e6eaDownload preserved edition · Document JSON

Supporting source editions

File_18 — Chronological Data TablesSource · 38-File_18.Chronological_Data_Tables-20260919-141048-.md
SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5Download preserved edition · Document JSON
File_09 — Cumulative ArchitectureSource · 30-File_09.Cumulative_Architecture-9-.md
SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876eDownload preserved edition · Document JSON

Complete numbered records

This list is for detailed inspection after the selected leads above. Each reading page preserves the original action and links its supporting evidence. The manifest supplies these links and edition hashes without copying document bodies.

C23 — The eight retained families on the ratio-and-scale systemDocument JSON · Download preserved record
SHA-256 75c94cb7d54531d7f46aa6c14d628bdc7b4b23d5237ec169f91b17e1bfbd9018
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C24 — One residual system behind the two descriptionsDocument JSON · Download preserved record
SHA-256 bf751c8a403dedea656180604d75a3aa2d76f930938a8b044c4d715e983da67b
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C25 — A compact endpoint form for the retained Mirror branchesDocument JSON · Download preserved record
SHA-256 2ad7720eeaea46a48b7b906d0fcf76e45544e13f1fb4a50588e7f3de7e8674d1
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C26 — Widths do not determine the branchDocument JSON · Download preserved record
SHA-256 ad959a8890dd9ea70cc1b2704fad2ebb76d59d348e361e8e4073c233b2708a56
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C27 — Civil-year counting agrees with the Mirror coordinatesDocument JSON · Download preserved record
SHA-256 d5d2b910181556edf111e974ed86fd8a51b3dcef6ea071f1a8906442fa6988d4
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C28 — 6877 is an off-centre subinterval of 8993Document JSON · Download preserved record
SHA-256 3d3d2c797a9df32dd6efec102e9bf83e774ba24d00999d129d01af2e49ba4834
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C29 — The canonical Mirror and local symmetry are different mapsDocument JSON · Download preserved record
SHA-256 c8f8c9d7055986add96eaace32a5a13f3c2f381f09c2c3acfe3114c900d8853b
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C30 — A two-year branch change reverses under reflectionDocument JSON · Download preserved record
SHA-256 eeac820007107efd393f25ec186fc8ff6dd4ec59301228edf7e255167cda7c9d
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C31 — The 23 and 529 patterns coexist without being identicalDocument JSON · Download preserved record
SHA-256 0305c759319c1b3cd568591a3cbfb37fde0e1287c2540661285bb88558528bb5
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C32 — Integer endpoints can have half-integer Mirror centresDocument JSON · Download preserved record
SHA-256 83cdaad833b7ffdf09dfa891890e4cd6fdf5da0841148896a28f06eb0dee4a2f
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C33 — A qualified 19-fold Mirror interval from cumulative Shem to NoahDocument JSON · Download preserved record
SHA-256 c493cf45d18559ee3f42ec0723653c096f27296573b4c8e69df097994e59dcb1
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C34 — Two 17-fold paths share a 15-fold intersectionDocument JSON · Download preserved record
SHA-256 fb5c71a1979b531fb29933dc295362b6970dfb70662648a78db4cba02585365d
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C35 — A reflected ON Shem endpoint extends the registered graphDocument JSON · Download preserved record
SHA-256 b03d4a27f7102cdbf7b37c1227981158f1978ea49259f0911fed18f7f7e9eb65
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C36 — The 12-fold family gains four right-hand placementsDocument JSON · Download preserved record
SHA-256 807d898578f21c4f87e100b1fa5c290030ddbf6f633c2dbacf2b9d6ad2373499
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C37 — 22-fold spans coexist with the full 6877 constructionsDocument JSON · Download preserved record
SHA-256 0dcfd483147882390b7bba737ddc0fb2edeea89ab35b809a1b14bca9dc9d2c4c
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C38 — A joined 24-fold Mirror path is admitted on N01Document JSON · Download preserved record
SHA-256 9ac61ef8a6e0fd72e897bf67d635de8239abfa76197ec659e0ef0cea075c163c
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C39 — The 24-fold and 20-fold intervals share a local centreDocument JSON · Download preserved record
SHA-256 6fb4dcbe7a055ea3d7dbd17624c4076e6dc49b5df562c58524ed7fbc0f2ab880
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C40 — One 24-fold path has five qualified two-part decompositionsDocument JSON · Download preserved record
SHA-256 5691276d6aee88e6bb788afaf350fe21b223a27ed493608b5be8ef4686e356a3
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C41 — Raw 24-fold pairs and the joined path have different domainsDocument JSON · Download preserved record
SHA-256 c703d27ce60a3a6d3bfb3046c928d7551c2f0171243016c8324ddeeb06bcbae7
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C42 — The full 6877 expansion joins 19 and 22, while 24 selects N01Document JSON · Download preserved record
SHA-256 c4962aba5889c06559dd0a8ba4d7fabfc3a6503a109707ae2271b9f0f5a2a8a1
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C43 — The extended typed graph has eleven selected family labelsDocument JSON · Download preserved record
SHA-256 e3b3e4582a306149b2af4aaa161d119ef53c24780e4a9b8850e608d8c680e6ea
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C44 — Two valid Shem members cannot be silently identifiedDocument JSON · Download preserved record
SHA-256 230a0116e466ee63a985b1ca9d0be04fa9478906ce6d5496c4465e386e3ce80c
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C45 — The ON endpoint is an essential binding of the new pathsDocument JSON · Download preserved record
SHA-256 38cdd8a739642e6a03a96a045e12f949148a511084238c266d142c991001946b
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C46 — The added families expose one already retained endpoint matchDocument JSON · Download preserved record
SHA-256 29eb86b1c4b59fa4ca9b2632d995f4be3938043fb9b66e7593c726ece26a1f6b
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C47 — Different errors leave different Mirror residualsDocument JSON · Download preserved record
SHA-256 5ba2591a810f405d17ca4092b815d8ba378bf09a9f23f10ce8681c73dd7dfcd7
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C48 — Source-only pairs extend farther than the joined constructionDocument JSON · Download preserved record
SHA-256 2017c270f45fe8de35f5008caa4a4f1f564151e8259c9bbd12f0cd9ba12e3fad
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C49 — 6877 sits inside 10051 with a 339-year centre offsetDocument JSON · Download preserved record
SHA-256 3a0730ff0af150e45ea0c05b98e0a4f4bc591b56ff7b7754a06e34b5ba8b45ed
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C50 — Endpoint atlas for the full 6877 constructionsDocument JSON · Download preserved record
SHA-256 6d4b13bf9e8a07fc16a13c07497b4a8cda6bf1e6a5d146b175dc00cb8223ac05
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C51 — Family closure alone is not a sufficient source certificateDocument JSON · Download preserved record
SHA-256 c60d9a79208173c936197844cbe547f74544fe4bc75ff01fb7d954b84ea95a7a
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e
C52 — Thirty-step Mirror synthesis: where 6877 belongsDocument JSON · Download preserved record
SHA-256 1d8418b2070995e686a5e4dad6301fe0fa0b28f235f1fc504b47b375df9bf484
Linked evidence (2)
- File 18SHA-256 68301ab760bfbe2e874aedc5c8d943ced7a6219d34bc2859332a70713f9630d5
- File 09SHA-256 45851004c5864229ebf6a896f9099819a08d8926715d3e97e4bc3985c4a3876e