{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IR7SEXLQIFNAN5HRUYLMAGXOUZ","short_pith_number":"pith:IR7SEXLQ","canonical_record":{"source":{"id":"1402.6391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-02-26T02:08:32Z","cross_cats_sorted":[],"title_canon_sha256":"ac5299dd302780f30104eeb5e93e49e91ea1cec0ec1a3f1aea92832cf3f34f8c","abstract_canon_sha256":"2948b1b20d4b4b2066d10319d88c2668bf25be1d37009bdce37925c18d7fc9f1"},"schema_version":"1.0"},"canonical_sha256":"447f225d70415a06f4f1a616c01aeea64a8f28fe6f4c016baffbca79f7ce7989","source":{"kind":"arxiv","id":"1402.6391","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6391","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6391v1","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6391","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"IR7SEXLQIFNA","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IR7SEXLQIFNAN5HR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IR7SEXLQ","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IR7SEXLQIFNAN5HRUYLMAGXOUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-02-26T02:08:32Z","cross_cats_sorted":[],"title_canon_sha256":"ac5299dd302780f30104eeb5e93e49e91ea1cec0ec1a3f1aea92832cf3f34f8c","abstract_canon_sha256":"2948b1b20d4b4b2066d10319d88c2668bf25be1d37009bdce37925c18d7fc9f1"},"schema_version":"1.0"},"canonical_sha256":"447f225d70415a06f4f1a616c01aeea64a8f28fe6f4c016baffbca79f7ce7989","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:44.622658Z","signature_b64":"14QNCuxm4OQ7jvLXsteE0zRGL/7HbKw+S9UyHnuRP8tXSwX5GfFYlhSuyP2eCgyZA+bPC4qY5W51IKJuwaqhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"447f225d70415a06f4f1a616c01aeea64a8f28fe6f4c016baffbca79f7ce7989","last_reissued_at":"2026-05-18T02:57:44.622167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:44.622167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6391","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":"2026-05-18T02:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XGydzWPvcneN5c2EZesLqbIzQkhG7krJJVLlQtrva+QOgWGEco4WuBHumAPqHArWnDnxujJMFm2IwtyJtV/LCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:04:41.975869Z"},"content_sha256":"9bdc46e17cbfb0327453055e4d285da9c09a6c49e86379ffea32ba725aaeaaa1","schema_version":"1.0","event_id":"sha256:9bdc46e17cbfb0327453055e4d285da9c09a6c49e86379ffea32ba725aaeaaa1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IR7SEXLQIFNAN5HRUYLMAGXOUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Hadwiger Theorem for Simplicial Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Matthew L. Wright, P. Christopher Staecker","submitted_at":"2014-02-26T02:08:32Z","abstract_excerpt":"We define the notion of valuation on simplicial maps between geometric realizations of simplicial complexes in $\\mathbb{R}^n$. Valuations on simplicial maps are analogous to valuations on sets. In particular, we define the Lefschetz volumes, which are analogous to the intrinsic volumes of subsets of $\\mathbb{R}^n$. Our definition not only provides a generalization of the Lefschetz number, but also yields a Hadwiger-style classification theorem for all such valuations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6391","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":"2026-05-18T02:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YKQukixTdfEiDIU3iUbYMIuG5IJfcOy5raNkTiJbcluQxp9p1RFlKJaT5Y0BMYosd4GFtduDZT8Bz6kSgbC4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:04:41.976197Z"},"content_sha256":"44a89ff0c99c93dd2134861ddd1c625ec24ce672d6d0d26ec8dedaf6b61c47d7","schema_version":"1.0","event_id":"sha256:44a89ff0c99c93dd2134861ddd1c625ec24ce672d6d0d26ec8dedaf6b61c47d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IR7SEXLQIFNAN5HRUYLMAGXOUZ/bundle.json","state_url":"https://pith.science/pith/IR7SEXLQIFNAN5HRUYLMAGXOUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IR7SEXLQIFNAN5HRUYLMAGXOUZ/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":"2026-06-26T20:04:41Z","links":{"resolver":"https://pith.science/pith/IR7SEXLQIFNAN5HRUYLMAGXOUZ","bundle":"https://pith.science/pith/IR7SEXLQIFNAN5HRUYLMAGXOUZ/bundle.json","state":"https://pith.science/pith/IR7SEXLQIFNAN5HRUYLMAGXOUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IR7SEXLQIFNAN5HRUYLMAGXOUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IR7SEXLQIFNAN5HRUYLMAGXOUZ","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":"2948b1b20d4b4b2066d10319d88c2668bf25be1d37009bdce37925c18d7fc9f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-02-26T02:08:32Z","title_canon_sha256":"ac5299dd302780f30104eeb5e93e49e91ea1cec0ec1a3f1aea92832cf3f34f8c"},"schema_version":"1.0","source":{"id":"1402.6391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6391","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6391v1","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6391","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"IR7SEXLQIFNA","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IR7SEXLQIFNAN5HR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IR7SEXLQ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:44a89ff0c99c93dd2134861ddd1c625ec24ce672d6d0d26ec8dedaf6b61c47d7","target":"graph","created_at":"2026-05-18T02:57:44Z","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 define the notion of valuation on simplicial maps between geometric realizations of simplicial complexes in $\\mathbb{R}^n$. Valuations on simplicial maps are analogous to valuations on sets. In particular, we define the Lefschetz volumes, which are analogous to the intrinsic volumes of subsets of $\\mathbb{R}^n$. Our definition not only provides a generalization of the Lefschetz number, but also yields a Hadwiger-style classification theorem for all such valuations.","authors_text":"Matthew L. Wright, P. Christopher Staecker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-02-26T02:08:32Z","title":"A Hadwiger Theorem for Simplicial Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6391","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":"sha256:9bdc46e17cbfb0327453055e4d285da9c09a6c49e86379ffea32ba725aaeaaa1","target":"record","created_at":"2026-05-18T02:57:44Z","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":"2948b1b20d4b4b2066d10319d88c2668bf25be1d37009bdce37925c18d7fc9f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-02-26T02:08:32Z","title_canon_sha256":"ac5299dd302780f30104eeb5e93e49e91ea1cec0ec1a3f1aea92832cf3f34f8c"},"schema_version":"1.0","source":{"id":"1402.6391","kind":"arxiv","version":1}},"canonical_sha256":"447f225d70415a06f4f1a616c01aeea64a8f28fe6f4c016baffbca79f7ce7989","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"447f225d70415a06f4f1a616c01aeea64a8f28fe6f4c016baffbca79f7ce7989","first_computed_at":"2026-05-18T02:57:44.622167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:44.622167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"14QNCuxm4OQ7jvLXsteE0zRGL/7HbKw+S9UyHnuRP8tXSwX5GfFYlhSuyP2eCgyZA+bPC4qY5W51IKJuwaqhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:44.622658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bdc46e17cbfb0327453055e4d285da9c09a6c49e86379ffea32ba725aaeaaa1","sha256:44a89ff0c99c93dd2134861ddd1c625ec24ce672d6d0d26ec8dedaf6b61c47d7"],"state_sha256":"e21905cc7d617bac3e6f1ef8b42f99092a3d6697368ac51525d29a7fee3d854d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/SeR+mKzlbPdYfoFqp8HwZb8RTfRcIR00G2TD0ubkcW2SwOsov9m/YpJWOmwa4iXpbW1VECir2aWcaHB3JQsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T20:04:41.978261Z","bundle_sha256":"bbe95a74d2ade27927c5d0b472ed2b90ae929827789f12ff89d3abb55306c145"}}