{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NLEIJA62HG4ZFRYAD4WBUWAPCG","short_pith_number":"pith:NLEIJA62","canonical_record":{"source":{"id":"2607.04289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-05T13:05:41Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b55caf6cd717839882f20e73c88add3effe5f7a99093231f9231b20de2d147bc","abstract_canon_sha256":"5958dbbe0e4d087a2c3bbf565876923d8fa6850bc1d273c3ec7e6e016f8235d5"},"schema_version":"1.0"},"canonical_sha256":"6ac88483da39b992c7001f2c1a580f11a6a7875ddfc39a79a710892465487ee6","source":{"kind":"arxiv","id":"2607.04289","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04289","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04289v1","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04289","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"NLEIJA62HG4Z","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_16","alias_value":"NLEIJA62HG4ZFRYA","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_8","alias_value":"NLEIJA62","created_at":"2026-07-07T02:19:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NLEIJA62HG4ZFRYAD4WBUWAPCG","target":"record","payload":{"canonical_record":{"source":{"id":"2607.04289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-05T13:05:41Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b55caf6cd717839882f20e73c88add3effe5f7a99093231f9231b20de2d147bc","abstract_canon_sha256":"5958dbbe0e4d087a2c3bbf565876923d8fa6850bc1d273c3ec7e6e016f8235d5"},"schema_version":"1.0"},"canonical_sha256":"6ac88483da39b992c7001f2c1a580f11a6a7875ddfc39a79a710892465487ee6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:19:07.135052Z","signature_b64":"TIKlW5Z6Gr1N3S75RE398Rl0i4Mg8DrLS25QYkJXdHAFHNZ+X9yMJ62j2Lv2dzBFSV0SQrRrkXMa/RvWjjWaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ac88483da39b992c7001f2c1a580f11a6a7875ddfc39a79a710892465487ee6","last_reissued_at":"2026-07-07T02:19:07.134283Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:19:07.134283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.04289","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-07T02:19:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFPScQ4p27Ik73i8B98Nm6OK+rDuRXCtc1KE0Iy9cG6KDDjh6xNS+3WKXyQ/EBv9Sd85ZtvOmMxXT4vGBzHTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:21:45.944598Z"},"content_sha256":"0e4274e1c8be2ec1e9560719fdeaea3e0be236ad23adf32cc5439d3f49286bb9","schema_version":"1.0","event_id":"sha256:0e4274e1c8be2ec1e9560719fdeaea3e0be236ad23adf32cc5439d3f49286bb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NLEIJA62HG4ZFRYAD4WBUWAPCG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chromatic Completeness and the Independence of Geometric Obstruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"quant-ph","authors_text":"Karl Svozil","submitted_at":"2026-07-05T13:05:41Z","abstract_excerpt":"We establish a strict logical separation between two distinct phenomena in orthogonality hypergraphs: chromatic completeness, the possibility of assigning a single globally consistent nondegenerate spectrum to all contexts, and geometric coordinatizability, the existence of a faithful orthogonal representation by rays. A strong chromatic number larger than the Hilbert-space dimension obstructs only the former. It does not, by itself, obstruct the existence of a faithful orthogonal representation. We make this separation explicit by comparing two three-dimensional examples with the same strong "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04289","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04289/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-07T02:19:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XQ+Vrozh3twp+e2ayAGwA8GO6axmC6UCqQvsU1NCLS6NMwjjSXR72YsKg0+5DAY6dvQGx2lJgEbpJsQMcj95AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:21:45.945165Z"},"content_sha256":"ee36fa9f7898f50efdfccde02ff02545806351f58560b3a29abe361c84d58a69","schema_version":"1.0","event_id":"sha256:ee36fa9f7898f50efdfccde02ff02545806351f58560b3a29abe361c84d58a69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NLEIJA62HG4ZFRYAD4WBUWAPCG/bundle.json","state_url":"https://pith.science/pith/NLEIJA62HG4ZFRYAD4WBUWAPCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NLEIJA62HG4ZFRYAD4WBUWAPCG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T14:21:45Z","links":{"resolver":"https://pith.science/pith/NLEIJA62HG4ZFRYAD4WBUWAPCG","bundle":"https://pith.science/pith/NLEIJA62HG4ZFRYAD4WBUWAPCG/bundle.json","state":"https://pith.science/pith/NLEIJA62HG4ZFRYAD4WBUWAPCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NLEIJA62HG4ZFRYAD4WBUWAPCG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NLEIJA62HG4ZFRYAD4WBUWAPCG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5958dbbe0e4d087a2c3bbf565876923d8fa6850bc1d273c3ec7e6e016f8235d5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-05T13:05:41Z","title_canon_sha256":"b55caf6cd717839882f20e73c88add3effe5f7a99093231f9231b20de2d147bc"},"schema_version":"1.0","source":{"id":"2607.04289","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04289","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04289v1","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04289","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"NLEIJA62HG4Z","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_16","alias_value":"NLEIJA62HG4ZFRYA","created_at":"2026-07-07T02:19:07Z"},{"alias_kind":"pith_short_8","alias_value":"NLEIJA62","created_at":"2026-07-07T02:19:07Z"}],"graph_snapshots":[{"event_id":"sha256:ee36fa9f7898f50efdfccde02ff02545806351f58560b3a29abe361c84d58a69","target":"graph","created_at":"2026-07-07T02:19:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.04289/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a strict logical separation between two distinct phenomena in orthogonality hypergraphs: chromatic completeness, the possibility of assigning a single globally consistent nondegenerate spectrum to all contexts, and geometric coordinatizability, the existence of a faithful orthogonal representation by rays. A strong chromatic number larger than the Hilbert-space dimension obstructs only the former. It does not, by itself, obstruct the existence of a faithful orthogonal representation. We make this separation explicit by comparing two three-dimensional examples with the same strong ","authors_text":"Karl Svozil","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-05T13:05:41Z","title":"Chromatic Completeness and the Independence of Geometric Obstruction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04289","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0e4274e1c8be2ec1e9560719fdeaea3e0be236ad23adf32cc5439d3f49286bb9","target":"record","created_at":"2026-07-07T02:19:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5958dbbe0e4d087a2c3bbf565876923d8fa6850bc1d273c3ec7e6e016f8235d5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-05T13:05:41Z","title_canon_sha256":"b55caf6cd717839882f20e73c88add3effe5f7a99093231f9231b20de2d147bc"},"schema_version":"1.0","source":{"id":"2607.04289","kind":"arxiv","version":1}},"canonical_sha256":"6ac88483da39b992c7001f2c1a580f11a6a7875ddfc39a79a710892465487ee6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ac88483da39b992c7001f2c1a580f11a6a7875ddfc39a79a710892465487ee6","first_computed_at":"2026-07-07T02:19:07.134283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:19:07.134283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TIKlW5Z6Gr1N3S75RE398Rl0i4Mg8DrLS25QYkJXdHAFHNZ+X9yMJ62j2Lv2dzBFSV0SQrRrkXMa/RvWjjWaCA==","signature_status":"signed_v1","signed_at":"2026-07-07T02:19:07.135052Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04289","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e4274e1c8be2ec1e9560719fdeaea3e0be236ad23adf32cc5439d3f49286bb9","sha256:ee36fa9f7898f50efdfccde02ff02545806351f58560b3a29abe361c84d58a69"],"state_sha256":"19b362c66496c970fee31e99f9b5ac30e3d67915822e3753768851160d157949"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nYOtW/ICXgm35xqel2w4DbrDscRBxfIfSlDLNZdGbMyaAZD+qNl4TWfaUfMHMk7zSXhRRLlUFk0yNlegnoV4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T14:21:45.979399Z","bundle_sha256":"25181217d770ce9f7c1da68ae30505341527afbce78272c91da5dc9a9ea14650"}}