{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JSTW6FVGZPS5GDZGOCHVNLQ7VW","short_pith_number":"pith:JSTW6FVG","canonical_record":{"source":{"id":"1505.04487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-18T01:41:20Z","cross_cats_sorted":[],"title_canon_sha256":"15da4a606ce2c562e83ec9ec80f27dd556136e75ca2ebca84121929eabe587c7","abstract_canon_sha256":"083a4a020b4366f7ef3644b54e3400edf5574c12d2c64ccd6e1f2e92d6cbade9"},"schema_version":"1.0"},"canonical_sha256":"4ca76f16a6cbe5d30f26708f56ae1fad9958bf7574e35ec280ab7cfc555fc19c","source":{"kind":"arxiv","id":"1505.04487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04487","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04487v1","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04487","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"pith_short_12","alias_value":"JSTW6FVGZPS5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JSTW6FVGZPS5GDZG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JSTW6FVG","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JSTW6FVGZPS5GDZGOCHVNLQ7VW","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-18T01:41:20Z","cross_cats_sorted":[],"title_canon_sha256":"15da4a606ce2c562e83ec9ec80f27dd556136e75ca2ebca84121929eabe587c7","abstract_canon_sha256":"083a4a020b4366f7ef3644b54e3400edf5574c12d2c64ccd6e1f2e92d6cbade9"},"schema_version":"1.0"},"canonical_sha256":"4ca76f16a6cbe5d30f26708f56ae1fad9958bf7574e35ec280ab7cfc555fc19c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:25.326393Z","signature_b64":"qeYG+MiEOBuwwWgQqFoNDzebLe/yw2Xb0Ue777dr071oibasQ4kcaMpPP9cxe1GGGpFGZA4RhbMO1z5F8Wd6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ca76f16a6cbe5d30f26708f56ae1fad9958bf7574e35ec280ab7cfc555fc19c","last_reissued_at":"2026-05-18T02:07:25.325999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:25.325999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04487","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":"2026-05-18T02:07:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2ZhGUTVxcw25/twkCWBMsaD+LTAhmfcq7Ipb145WmYl8zZBWZ81QqOiM2shu4+zqDORlq+X+lyEeJU+wPdzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:27:28.973128Z"},"content_sha256":"8f4746be9da8e5b3202f2c801cd19f283db65ec6e3d5573c36c8d2758d6222a8","schema_version":"1.0","event_id":"sha256:8f4746be9da8e5b3202f2c801cd19f283db65ec6e3d5573c36c8d2758d6222a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JSTW6FVGZPS5GDZGOCHVNLQ7VW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tetrachromagea","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jimmy Dillies","submitted_at":"2015-05-18T01:41:20Z","abstract_excerpt":"We construct a moduli space of four colorings on planar cubic graphs. More precisely, we introduce the notion of weak Hamiltonian, a generalization of Hamiltonian cycles, and relate it to 4-colorings. Weak Hamiltonians have a form of deformation, which we call mutation, which gives them a graph structure, the Weak Hamiltonian graph. This graph encodes the different colorings as 3 vertex cliques. Identifying vertices on these cliques, we obtain a new graph, the chromatic graph, whose vertices are exactly the colorings of the original graph. Also, this construction gives a heuristic argument on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04487","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":""},"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":"2026-05-18T02:07:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rgRW6zfGgh6tPyq3AAA+YGvkZ6JzKUuOA5cpV82UQPs8Dg57zr+YI90ppJXfX9lVHs3SJn8/0ZCPcxSrYB3dAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:27:28.973498Z"},"content_sha256":"bddfaa6f06a7086be4a3ec788b16dcb1df041919ded3714c58b950ed2de11595","schema_version":"1.0","event_id":"sha256:bddfaa6f06a7086be4a3ec788b16dcb1df041919ded3714c58b950ed2de11595"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JSTW6FVGZPS5GDZGOCHVNLQ7VW/bundle.json","state_url":"https://pith.science/pith/JSTW6FVGZPS5GDZGOCHVNLQ7VW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JSTW6FVGZPS5GDZGOCHVNLQ7VW/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":"2026-06-23T05:27:28Z","links":{"resolver":"https://pith.science/pith/JSTW6FVGZPS5GDZGOCHVNLQ7VW","bundle":"https://pith.science/pith/JSTW6FVGZPS5GDZGOCHVNLQ7VW/bundle.json","state":"https://pith.science/pith/JSTW6FVGZPS5GDZGOCHVNLQ7VW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JSTW6FVGZPS5GDZGOCHVNLQ7VW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JSTW6FVGZPS5GDZGOCHVNLQ7VW","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":"083a4a020b4366f7ef3644b54e3400edf5574c12d2c64ccd6e1f2e92d6cbade9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-18T01:41:20Z","title_canon_sha256":"15da4a606ce2c562e83ec9ec80f27dd556136e75ca2ebca84121929eabe587c7"},"schema_version":"1.0","source":{"id":"1505.04487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04487","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04487v1","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04487","created_at":"2026-05-18T02:07:25Z"},{"alias_kind":"pith_short_12","alias_value":"JSTW6FVGZPS5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JSTW6FVGZPS5GDZG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JSTW6FVG","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:bddfaa6f06a7086be4a3ec788b16dcb1df041919ded3714c58b950ed2de11595","target":"graph","created_at":"2026-05-18T02:07:25Z","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"},"paper":{"abstract_excerpt":"We construct a moduli space of four colorings on planar cubic graphs. More precisely, we introduce the notion of weak Hamiltonian, a generalization of Hamiltonian cycles, and relate it to 4-colorings. Weak Hamiltonians have a form of deformation, which we call mutation, which gives them a graph structure, the Weak Hamiltonian graph. This graph encodes the different colorings as 3 vertex cliques. Identifying vertices on these cliques, we obtain a new graph, the chromatic graph, whose vertices are exactly the colorings of the original graph. Also, this construction gives a heuristic argument on ","authors_text":"Jimmy Dillies","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-18T01:41:20Z","title":"Tetrachromagea"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04487","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":"sha256:8f4746be9da8e5b3202f2c801cd19f283db65ec6e3d5573c36c8d2758d6222a8","target":"record","created_at":"2026-05-18T02:07:25Z","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":"083a4a020b4366f7ef3644b54e3400edf5574c12d2c64ccd6e1f2e92d6cbade9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-18T01:41:20Z","title_canon_sha256":"15da4a606ce2c562e83ec9ec80f27dd556136e75ca2ebca84121929eabe587c7"},"schema_version":"1.0","source":{"id":"1505.04487","kind":"arxiv","version":1}},"canonical_sha256":"4ca76f16a6cbe5d30f26708f56ae1fad9958bf7574e35ec280ab7cfc555fc19c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ca76f16a6cbe5d30f26708f56ae1fad9958bf7574e35ec280ab7cfc555fc19c","first_computed_at":"2026-05-18T02:07:25.325999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:25.325999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qeYG+MiEOBuwwWgQqFoNDzebLe/yw2Xb0Ue777dr071oibasQ4kcaMpPP9cxe1GGGpFGZA4RhbMO1z5F8Wd6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:25.326393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f4746be9da8e5b3202f2c801cd19f283db65ec6e3d5573c36c8d2758d6222a8","sha256:bddfaa6f06a7086be4a3ec788b16dcb1df041919ded3714c58b950ed2de11595"],"state_sha256":"972e4cc607849d27c16cf01b7bd9956525cceea03c4be6fc5137c4e8fd7ce51d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dt2bqZf0BuiLRHENYZdvRwQ+md94WFkP0NWVzBjVg+wBIK+5XzhGeS0Q4J7oiDuJMdQrdBGOXPlBF9Lo2uzACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:27:28.975457Z","bundle_sha256":"ffdb455c007fe6464e88060631435d1c27fdcb9ea341dd47727604974817dacc"}}