{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NKNUSP42ZI5XH53WNUZB3CEJLM","short_pith_number":"pith:NKNUSP42","canonical_record":{"source":{"id":"1303.4276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-03-18T15:01:16Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cdef83661134be5bd2afda19b21af6f36f219679fa1b86c5961ed703884bed34","abstract_canon_sha256":"63532753985dcf95ea65fef2428e1ff65822ab75fb4547de824ea3427576554c"},"schema_version":"1.0"},"canonical_sha256":"6a9b493f9aca3b73f7766d321d88895b3d8e7785cbe905e67968fce542929288","source":{"kind":"arxiv","id":"1303.4276","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4276","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4276v1","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4276","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"NKNUSP42ZI5X","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NKNUSP42ZI5XH53W","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NKNUSP42","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NKNUSP42ZI5XH53WNUZB3CEJLM","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-03-18T15:01:16Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cdef83661134be5bd2afda19b21af6f36f219679fa1b86c5961ed703884bed34","abstract_canon_sha256":"63532753985dcf95ea65fef2428e1ff65822ab75fb4547de824ea3427576554c"},"schema_version":"1.0"},"canonical_sha256":"6a9b493f9aca3b73f7766d321d88895b3d8e7785cbe905e67968fce542929288","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:39.001357Z","signature_b64":"FDY2LDbUi7b8YCkEaXqLnmuqe43cej75B7FRICcc8wgzA2opmDYY3xG3+O2Kp4NjXf/YluAOc6IRlxYxv/INCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a9b493f9aca3b73f7766d321d88895b3d8e7785cbe905e67968fce542929288","last_reissued_at":"2026-05-18T03:30:39.000404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:39.000404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4276","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":"2026-05-18T03:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ufo9qUqe9ARruIGebyvmfW/Y7WNyypU6lGS5Rz9/jRL06MCflxCn+6kq7kSFe7KS8sfsgMr+Xycwdfdx7+xCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:18:19.860566Z"},"content_sha256":"5c58f46fdf9a4ad94595d9461fa67d796adb0db9657eb6860116ed1753d44946","schema_version":"1.0","event_id":"sha256:5c58f46fdf9a4ad94595d9461fa67d796adb0db9657eb6860116ed1753d44946"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NKNUSP42ZI5XH53WNUZB3CEJLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive Topological Quantum Field Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Markus Banagl","submitted_at":"2013-03-18T15:01:16Z","abstract_excerpt":"We propose a new notion of positivity for topological field theories (TFTs), based on S. Eilenberg's concept of completeness for semirings. We show that a complete ground semiring, a system of fields on manifolds and a system of action functionals on these fields determine a positive TFT. The main feature of such a theory is a semiring-valued topologically invariant state sum that satisfies a gluing formula. The abstract framework has been carefully designed to cover a wide range of phenomena. For instance, we derive Polya's counting theory in combinatorics from state sum identities in a suita"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4276","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":"2026-05-18T03:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PCMEEOdX5kuRgrpOoPJCF9wZrY/ueM0RzwVv1tEm5Dx0/G534+bMHvD1UGKcNYFsciW4tJx1b2fwsI7x8+OBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:18:19.860915Z"},"content_sha256":"97d9b35ace434458cc59a39e9f5568bab93df388ac6c3bcda812ba9fc7156ac6","schema_version":"1.0","event_id":"sha256:97d9b35ace434458cc59a39e9f5568bab93df388ac6c3bcda812ba9fc7156ac6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKNUSP42ZI5XH53WNUZB3CEJLM/bundle.json","state_url":"https://pith.science/pith/NKNUSP42ZI5XH53WNUZB3CEJLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKNUSP42ZI5XH53WNUZB3CEJLM/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":"2026-05-28T02:18:19Z","links":{"resolver":"https://pith.science/pith/NKNUSP42ZI5XH53WNUZB3CEJLM","bundle":"https://pith.science/pith/NKNUSP42ZI5XH53WNUZB3CEJLM/bundle.json","state":"https://pith.science/pith/NKNUSP42ZI5XH53WNUZB3CEJLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKNUSP42ZI5XH53WNUZB3CEJLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NKNUSP42ZI5XH53WNUZB3CEJLM","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":"63532753985dcf95ea65fef2428e1ff65822ab75fb4547de824ea3427576554c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-03-18T15:01:16Z","title_canon_sha256":"cdef83661134be5bd2afda19b21af6f36f219679fa1b86c5961ed703884bed34"},"schema_version":"1.0","source":{"id":"1303.4276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4276","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4276v1","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4276","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"NKNUSP42ZI5X","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NKNUSP42ZI5XH53W","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NKNUSP42","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:97d9b35ace434458cc59a39e9f5568bab93df388ac6c3bcda812ba9fc7156ac6","target":"graph","created_at":"2026-05-18T03:30:39Z","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 propose a new notion of positivity for topological field theories (TFTs), based on S. Eilenberg's concept of completeness for semirings. We show that a complete ground semiring, a system of fields on manifolds and a system of action functionals on these fields determine a positive TFT. The main feature of such a theory is a semiring-valued topologically invariant state sum that satisfies a gluing formula. The abstract framework has been carefully designed to cover a wide range of phenomena. For instance, we derive Polya's counting theory in combinatorics from state sum identities in a suita","authors_text":"Markus Banagl","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-03-18T15:01:16Z","title":"Positive Topological Quantum Field Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4276","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":"sha256:5c58f46fdf9a4ad94595d9461fa67d796adb0db9657eb6860116ed1753d44946","target":"record","created_at":"2026-05-18T03:30:39Z","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":"63532753985dcf95ea65fef2428e1ff65822ab75fb4547de824ea3427576554c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-03-18T15:01:16Z","title_canon_sha256":"cdef83661134be5bd2afda19b21af6f36f219679fa1b86c5961ed703884bed34"},"schema_version":"1.0","source":{"id":"1303.4276","kind":"arxiv","version":1}},"canonical_sha256":"6a9b493f9aca3b73f7766d321d88895b3d8e7785cbe905e67968fce542929288","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a9b493f9aca3b73f7766d321d88895b3d8e7785cbe905e67968fce542929288","first_computed_at":"2026-05-18T03:30:39.000404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:39.000404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FDY2LDbUi7b8YCkEaXqLnmuqe43cej75B7FRICcc8wgzA2opmDYY3xG3+O2Kp4NjXf/YluAOc6IRlxYxv/INCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:39.001357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c58f46fdf9a4ad94595d9461fa67d796adb0db9657eb6860116ed1753d44946","sha256:97d9b35ace434458cc59a39e9f5568bab93df388ac6c3bcda812ba9fc7156ac6"],"state_sha256":"36a8f6f2dd61e5f365ea49fde27817c27d71f46551f2b69fad0a17c003eb3ffa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GAzg/vT6F399b6byoRx0Fy7RzaxKpczcBtJqm2N3wbLfXXFXPJq4uODdd0PuriwmJ918DyVa0y1h/Ko7oO25Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:18:19.862898Z","bundle_sha256":"fa14ebc897e1fe2f01d91ed5b4933ed9c839e409573df427a1ca50db62dc74aa"}}