{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:L75UXBLK4SS5CGART2RUEYLOIW","short_pith_number":"pith:L75UXBLK","canonical_record":{"source":{"id":"1707.09799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-31T10:53:49Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"356f69a5c9ed3f578d76914f3ec52d01dcb34e1fec868aa17de11a4d19150ba2","abstract_canon_sha256":"78c974d84931baa30841f7559a2b302b96c1deccf1beae39c8a6fa9dceac60e2"},"schema_version":"1.0"},"canonical_sha256":"5ffb4b856ae4a5d118119ea342616e459f621249305570b9609b89b26dbf4c24","source":{"kind":"arxiv","id":"1707.09799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09799","created_at":"2026-05-18T00:39:08Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09799v1","created_at":"2026-05-18T00:39:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09799","created_at":"2026-05-18T00:39:08Z"},{"alias_kind":"pith_short_12","alias_value":"L75UXBLK4SS5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L75UXBLK4SS5CGAR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L75UXBLK","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:L75UXBLK4SS5CGART2RUEYLOIW","target":"record","payload":{"canonical_record":{"source":{"id":"1707.09799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-31T10:53:49Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"356f69a5c9ed3f578d76914f3ec52d01dcb34e1fec868aa17de11a4d19150ba2","abstract_canon_sha256":"78c974d84931baa30841f7559a2b302b96c1deccf1beae39c8a6fa9dceac60e2"},"schema_version":"1.0"},"canonical_sha256":"5ffb4b856ae4a5d118119ea342616e459f621249305570b9609b89b26dbf4c24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:08.196711Z","signature_b64":"9QmfTD/SkX3gD0TWnPyCjy7PUl3u3yjsfShcpSa0OyA3Eksghz4DRSWLWtpW+Lc5X7tFjMuwLD3aa6WTCR4kBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ffb4b856ae4a5d118119ea342616e459f621249305570b9609b89b26dbf4c24","last_reissued_at":"2026-05-18T00:39:08.196030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:08.196030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.09799","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":"2026-05-18T00:39:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5cvf/6+a7oDkYR6mvMXiBo6yzafaZMwFneRp0dMVKDrT8cBAYZJsum6dclT4qN/xqaQu8kkjQP+ex9arUfVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:21:16.927138Z"},"content_sha256":"566c1856559714dbbddb42d750d524b0000def8a945e1b9ca9957d0c2de21aea","schema_version":"1.0","event_id":"sha256:566c1856559714dbbddb42d750d524b0000def8a945e1b9ca9957d0c2de21aea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:L75UXBLK4SS5CGART2RUEYLOIW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Axioms for the fixed point index of n-valued maps, and some applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AT","authors_text":"P. Christopher Staecker","submitted_at":"2017-07-31T10:53:49Z","abstract_excerpt":"We give an axiomatic characterization of the fixed point index of an $n$-valued map. For $n$-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopy invariance, additivity, and a splitting property. This uniqueness is used to obtain easy proofs of an averaging formula and product formula for the index. In the setting of $n$-valued maps on a manifold, we show that the axioms can be weakened."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09799","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":"2026-05-18T00:39:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZ0E0LtR6NRRFOakXKSWuXwlypfpDVSRObHRYOvQHGwO+LlPN3R7G5Fj5ZqF0gyyONOoQvwZIyg7LsEV0CTFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:21:16.927495Z"},"content_sha256":"d32db89fbc51f8b0a0de6ae3473dbc50d0408e829aa09508bca2b15cb0cee72a","schema_version":"1.0","event_id":"sha256:d32db89fbc51f8b0a0de6ae3473dbc50d0408e829aa09508bca2b15cb0cee72a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L75UXBLK4SS5CGART2RUEYLOIW/bundle.json","state_url":"https://pith.science/pith/L75UXBLK4SS5CGART2RUEYLOIW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L75UXBLK4SS5CGART2RUEYLOIW/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":"2026-06-26T22:21:16Z","links":{"resolver":"https://pith.science/pith/L75UXBLK4SS5CGART2RUEYLOIW","bundle":"https://pith.science/pith/L75UXBLK4SS5CGART2RUEYLOIW/bundle.json","state":"https://pith.science/pith/L75UXBLK4SS5CGART2RUEYLOIW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L75UXBLK4SS5CGART2RUEYLOIW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:L75UXBLK4SS5CGART2RUEYLOIW","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":"78c974d84931baa30841f7559a2b302b96c1deccf1beae39c8a6fa9dceac60e2","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-31T10:53:49Z","title_canon_sha256":"356f69a5c9ed3f578d76914f3ec52d01dcb34e1fec868aa17de11a4d19150ba2"},"schema_version":"1.0","source":{"id":"1707.09799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.09799","created_at":"2026-05-18T00:39:08Z"},{"alias_kind":"arxiv_version","alias_value":"1707.09799v1","created_at":"2026-05-18T00:39:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09799","created_at":"2026-05-18T00:39:08Z"},{"alias_kind":"pith_short_12","alias_value":"L75UXBLK4SS5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L75UXBLK4SS5CGAR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L75UXBLK","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:d32db89fbc51f8b0a0de6ae3473dbc50d0408e829aa09508bca2b15cb0cee72a","target":"graph","created_at":"2026-05-18T00:39:08Z","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 an axiomatic characterization of the fixed point index of an $n$-valued map. For $n$-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopy invariance, additivity, and a splitting property. This uniqueness is used to obtain easy proofs of an averaging formula and product formula for the index. In the setting of $n$-valued maps on a manifold, we show that the axioms can be weakened.","authors_text":"P. Christopher Staecker","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-31T10:53:49Z","title":"Axioms for the fixed point index of n-valued maps, and some applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09799","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":"sha256:566c1856559714dbbddb42d750d524b0000def8a945e1b9ca9957d0c2de21aea","target":"record","created_at":"2026-05-18T00:39:08Z","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":"78c974d84931baa30841f7559a2b302b96c1deccf1beae39c8a6fa9dceac60e2","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-31T10:53:49Z","title_canon_sha256":"356f69a5c9ed3f578d76914f3ec52d01dcb34e1fec868aa17de11a4d19150ba2"},"schema_version":"1.0","source":{"id":"1707.09799","kind":"arxiv","version":1}},"canonical_sha256":"5ffb4b856ae4a5d118119ea342616e459f621249305570b9609b89b26dbf4c24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ffb4b856ae4a5d118119ea342616e459f621249305570b9609b89b26dbf4c24","first_computed_at":"2026-05-18T00:39:08.196030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:08.196030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9QmfTD/SkX3gD0TWnPyCjy7PUl3u3yjsfShcpSa0OyA3Eksghz4DRSWLWtpW+Lc5X7tFjMuwLD3aa6WTCR4kBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:08.196711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.09799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:566c1856559714dbbddb42d750d524b0000def8a945e1b9ca9957d0c2de21aea","sha256:d32db89fbc51f8b0a0de6ae3473dbc50d0408e829aa09508bca2b15cb0cee72a"],"state_sha256":"83622a25040f1a6ea49b190aabf7958ee9a9cf62c60d0899429697f38be2f8d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZhOxqeMMWRARJvilAttpeHK9L45kBHV+VF05Fixro1QUEtHPCKchhEnImAd0XfOpTgV0eOrMbMdkcCWjzz5+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T22:21:16.929405Z","bundle_sha256":"4fc955e84011c65bb5e90eb20251bdf877b004d2ba53511c7bb5df6e2e86583a"}}