{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NVGNR47JR5FWZKLSO7UX4FGAT5","short_pith_number":"pith:NVGNR47J","canonical_record":{"source":{"id":"1006.5220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-06-27T16:21:29Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fbb39ad85e8a41d2a4b867f21e160ba95cbb7343327b8ec03a48f6607496d88e","abstract_canon_sha256":"1afd1897b796bbbca943276685debf6df5188fdfba2bc057c8389d403c3bb17d"},"schema_version":"1.0"},"canonical_sha256":"6d4cd8f3e98f4b6ca97277e97e14c09f4ea2ad970b2461cb7292b62f03edc819","source":{"kind":"arxiv","id":"1006.5220","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5220","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5220v2","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5220","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"NVGNR47JR5FW","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NVGNR47JR5FWZKLS","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NVGNR47J","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NVGNR47JR5FWZKLSO7UX4FGAT5","target":"record","payload":{"canonical_record":{"source":{"id":"1006.5220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-06-27T16:21:29Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"fbb39ad85e8a41d2a4b867f21e160ba95cbb7343327b8ec03a48f6607496d88e","abstract_canon_sha256":"1afd1897b796bbbca943276685debf6df5188fdfba2bc057c8389d403c3bb17d"},"schema_version":"1.0"},"canonical_sha256":"6d4cd8f3e98f4b6ca97277e97e14c09f4ea2ad970b2461cb7292b62f03edc819","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:13.937559Z","signature_b64":"C+L0B/mP7xZbmxsxMM4YnrFL0/RBtD7WVCADjZUZ3YJ1Q3OaOkCabB38R7ukEV41iOkqQevIseYJXaL9UWYiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d4cd8f3e98f4b6ca97277e97e14c09f4ea2ad970b2461cb7292b62f03edc819","last_reissued_at":"2026-05-18T04:41:13.937106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:13.937106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.5220","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6E2K1P6h58Z7bItQPW1/wNAPJs83wJHXeoLL3VD0l+U/WC9XnOnkSGI4RRo6fZvguLGyc+Q4uYq0KJN564DlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:06:47.991658Z"},"content_sha256":"34e483d686c8a2bf144aacf661e77d32ef7d6c7213584c2b0839b22c1d4636fe","schema_version":"1.0","event_id":"sha256:34e483d686c8a2bf144aacf661e77d32ef7d6c7213584c2b0839b22c1d4636fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NVGNR47JR5FWZKLSO7UX4FGAT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maps on graphs can be deformed to be coincidence-free","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GN","authors_text":"P. Christopher Staecker","submitted_at":"2010-06-27T16:21:29Z","abstract_excerpt":"We give a construction to remove coincidence points of continuous maps on graphs (1-complexes) by changing the maps by homotopies. When the codomain is not homeomorphic to the circle, we show that any pair of maps can be changed by homotopies to be coincidence free. This means that there can be no nontrivial coincidence index, Nielsen coincidence number, or coincidence Reidemeister trace in this setting, and the results of our previous paper \"A formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles\" are invalid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5220","kind":"arxiv","version":2},"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":"2026-05-18T04:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Cun/fLsXq5kc9Y+ifl4CnjCAPJmiIfPUl0KePg1zulG5Ot2a5GB8C0BGWfTeI281XI0Mq+udnnUm3vzz5HqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:06:47.992011Z"},"content_sha256":"48a4162589d5303b88c75c26e0d39471d727a4329c2d90d43fedaea975d32f54","schema_version":"1.0","event_id":"sha256:48a4162589d5303b88c75c26e0d39471d727a4329c2d90d43fedaea975d32f54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NVGNR47JR5FWZKLSO7UX4FGAT5/bundle.json","state_url":"https://pith.science/pith/NVGNR47JR5FWZKLSO7UX4FGAT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NVGNR47JR5FWZKLSO7UX4FGAT5/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":"2026-06-04T06:06:47Z","links":{"resolver":"https://pith.science/pith/NVGNR47JR5FWZKLSO7UX4FGAT5","bundle":"https://pith.science/pith/NVGNR47JR5FWZKLSO7UX4FGAT5/bundle.json","state":"https://pith.science/pith/NVGNR47JR5FWZKLSO7UX4FGAT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NVGNR47JR5FWZKLSO7UX4FGAT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NVGNR47JR5FWZKLSO7UX4FGAT5","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":"1afd1897b796bbbca943276685debf6df5188fdfba2bc057c8389d403c3bb17d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-06-27T16:21:29Z","title_canon_sha256":"fbb39ad85e8a41d2a4b867f21e160ba95cbb7343327b8ec03a48f6607496d88e"},"schema_version":"1.0","source":{"id":"1006.5220","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5220","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5220v2","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5220","created_at":"2026-05-18T04:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"NVGNR47JR5FW","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NVGNR47JR5FWZKLS","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NVGNR47J","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:48a4162589d5303b88c75c26e0d39471d727a4329c2d90d43fedaea975d32f54","target":"graph","created_at":"2026-05-18T04:41:13Z","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 give a construction to remove coincidence points of continuous maps on graphs (1-complexes) by changing the maps by homotopies. When the codomain is not homeomorphic to the circle, we show that any pair of maps can be changed by homotopies to be coincidence free. This means that there can be no nontrivial coincidence index, Nielsen coincidence number, or coincidence Reidemeister trace in this setting, and the results of our previous paper \"A formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles\" are invalid.","authors_text":"P. Christopher Staecker","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-06-27T16:21:29Z","title":"Maps on graphs can be deformed to be coincidence-free"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5220","kind":"arxiv","version":2},"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":"sha256:34e483d686c8a2bf144aacf661e77d32ef7d6c7213584c2b0839b22c1d4636fe","target":"record","created_at":"2026-05-18T04:41:13Z","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":"1afd1897b796bbbca943276685debf6df5188fdfba2bc057c8389d403c3bb17d","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-06-27T16:21:29Z","title_canon_sha256":"fbb39ad85e8a41d2a4b867f21e160ba95cbb7343327b8ec03a48f6607496d88e"},"schema_version":"1.0","source":{"id":"1006.5220","kind":"arxiv","version":2}},"canonical_sha256":"6d4cd8f3e98f4b6ca97277e97e14c09f4ea2ad970b2461cb7292b62f03edc819","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d4cd8f3e98f4b6ca97277e97e14c09f4ea2ad970b2461cb7292b62f03edc819","first_computed_at":"2026-05-18T04:41:13.937106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:13.937106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C+L0B/mP7xZbmxsxMM4YnrFL0/RBtD7WVCADjZUZ3YJ1Q3OaOkCabB38R7ukEV41iOkqQevIseYJXaL9UWYiCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:13.937559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5220","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34e483d686c8a2bf144aacf661e77d32ef7d6c7213584c2b0839b22c1d4636fe","sha256:48a4162589d5303b88c75c26e0d39471d727a4329c2d90d43fedaea975d32f54"],"state_sha256":"7f11b0932a6771c73027512597d5ee59160fa94591f0a14674d58dfe74302ddc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gtFQ4JR9fvK8PXiujJoBNNDAPIRxs9N5YWv3XH69A5iZeHbrmc6JI92yz2TRkn6UePPIsWJj6TpJjRlOzszNCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:06:47.993973Z","bundle_sha256":"5f3ff9b289e8eb7dfb9a3d8fc3b8ff67dd1fbdd2f28e3c39386ee61caedef178"}}