{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q4RZVTHAYBCNTPP3MFIMPLKF3I","short_pith_number":"pith:Q4RZVTHA","canonical_record":{"source":{"id":"1102.1223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-02-07T02:05:53Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"7a1018bf953a42905b843ddc26e100b850b42495c994038672253c5a33c59887","abstract_canon_sha256":"2a96767cd705859ae610d7fb9270d15edc06a608ee97032016fdbaf314c99c78"},"schema_version":"1.0"},"canonical_sha256":"87239acce0c044d9bdfb6150c7ad45da18851b67160886e63df448ac72c6ce8b","source":{"kind":"arxiv","id":"1102.1223","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1223","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1223v1","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1223","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"Q4RZVTHAYBCN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q4RZVTHAYBCNTPP3","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q4RZVTHA","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q4RZVTHAYBCNTPP3MFIMPLKF3I","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-02-07T02:05:53Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"7a1018bf953a42905b843ddc26e100b850b42495c994038672253c5a33c59887","abstract_canon_sha256":"2a96767cd705859ae610d7fb9270d15edc06a608ee97032016fdbaf314c99c78"},"schema_version":"1.0"},"canonical_sha256":"87239acce0c044d9bdfb6150c7ad45da18851b67160886e63df448ac72c6ce8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:54.727449Z","signature_b64":"2QwW8OhPkTQ2nf2f3LEzIsLiKcPQMJ1vRHf1pqMWG8l5iA0P+qAYd3e+ir9zLP1ar2t9GIe+r1BFJWnpAFpCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87239acce0c044d9bdfb6150c7ad45da18851b67160886e63df448ac72c6ce8b","last_reissued_at":"2026-05-18T04:29:54.726604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:54.726604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1223","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":"2026-05-18T04:29:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jHG21vvimnOGqn0r6D6hyxqGyROV9ng2zWiAFgp7kOLuCZbkO00v/B0mgzB5Uomz7N3qTfQD9vfs3XIK8EMZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:46:25.997614Z"},"content_sha256":"33230c26bb09801859616cea0cb543fb36723edd78e0161394d9460639eb5b0e","schema_version":"1.0","event_id":"sha256:33230c26bb09801859616cea0cb543fb36723edd78e0161394d9460639eb5b0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q4RZVTHAYBCNTPP3MFIMPLKF3I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Axioms for the coincidence index of maps between manifolds of the same dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AT","authors_text":"Daciberg L. Goncalves, P. Christopher Staecker","submitted_at":"2011-02-07T02:05:53Z","abstract_excerpt":"We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in $\\Z\\oplus \\Z_2$. We also show in each setting that the group of values for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1223","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":"2026-05-18T04:29:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TNeSqT3PN3KjXs/TGJzlr4zy0Wu561+skBysrAPGVlcqmNT1y1LHryc3lJeeWlfn3nv/hXeOzyKQa9xTpBoUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:46:25.998329Z"},"content_sha256":"25648fcb4e7fe87dbe6f11a1fbaa623798b8915e07e6056b789609884e6f6dfe","schema_version":"1.0","event_id":"sha256:25648fcb4e7fe87dbe6f11a1fbaa623798b8915e07e6056b789609884e6f6dfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4RZVTHAYBCNTPP3MFIMPLKF3I/bundle.json","state_url":"https://pith.science/pith/Q4RZVTHAYBCNTPP3MFIMPLKF3I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4RZVTHAYBCNTPP3MFIMPLKF3I/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":"2026-06-04T04:46:26Z","links":{"resolver":"https://pith.science/pith/Q4RZVTHAYBCNTPP3MFIMPLKF3I","bundle":"https://pith.science/pith/Q4RZVTHAYBCNTPP3MFIMPLKF3I/bundle.json","state":"https://pith.science/pith/Q4RZVTHAYBCNTPP3MFIMPLKF3I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4RZVTHAYBCNTPP3MFIMPLKF3I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q4RZVTHAYBCNTPP3MFIMPLKF3I","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":"2a96767cd705859ae610d7fb9270d15edc06a608ee97032016fdbaf314c99c78","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-02-07T02:05:53Z","title_canon_sha256":"7a1018bf953a42905b843ddc26e100b850b42495c994038672253c5a33c59887"},"schema_version":"1.0","source":{"id":"1102.1223","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1223","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1223v1","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1223","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"Q4RZVTHAYBCN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q4RZVTHAYBCNTPP3","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q4RZVTHA","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:25648fcb4e7fe87dbe6f11a1fbaa623798b8915e07e6056b789609884e6f6dfe","target":"graph","created_at":"2026-05-18T04:29:54Z","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 study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in $\\Z\\oplus \\Z_2$. We also show in each setting that the group of values for t","authors_text":"Daciberg L. Goncalves, P. Christopher Staecker","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-02-07T02:05:53Z","title":"Axioms for the coincidence index of maps between manifolds of the same dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1223","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":"sha256:33230c26bb09801859616cea0cb543fb36723edd78e0161394d9460639eb5b0e","target":"record","created_at":"2026-05-18T04:29:54Z","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":"2a96767cd705859ae610d7fb9270d15edc06a608ee97032016fdbaf314c99c78","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-02-07T02:05:53Z","title_canon_sha256":"7a1018bf953a42905b843ddc26e100b850b42495c994038672253c5a33c59887"},"schema_version":"1.0","source":{"id":"1102.1223","kind":"arxiv","version":1}},"canonical_sha256":"87239acce0c044d9bdfb6150c7ad45da18851b67160886e63df448ac72c6ce8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87239acce0c044d9bdfb6150c7ad45da18851b67160886e63df448ac72c6ce8b","first_computed_at":"2026-05-18T04:29:54.726604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:54.726604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2QwW8OhPkTQ2nf2f3LEzIsLiKcPQMJ1vRHf1pqMWG8l5iA0P+qAYd3e+ir9zLP1ar2t9GIe+r1BFJWnpAFpCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:54.727449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1223","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33230c26bb09801859616cea0cb543fb36723edd78e0161394d9460639eb5b0e","sha256:25648fcb4e7fe87dbe6f11a1fbaa623798b8915e07e6056b789609884e6f6dfe"],"state_sha256":"12ee2d42b4739b412488de4bc83c6ea80dd94bea740e92654ee26ffbc20723f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qvj01oQzFY0SCzLIwE9q2F8ipjxuDRNMb4I75dKuBjq0d7IH3NAbEREwt1XyihnzIucL0lrizFgHyEYgS1wKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:46:26.002353Z","bundle_sha256":"ce8ccc7f2c1e0a3ba7fd03a396e7f9a0039fb3183bbeb744ad578e56787639ae"}}