{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EX4KXK7LJAX6A6KMV4WEGP5Y4N","short_pith_number":"pith:EX4KXK7L","canonical_record":{"source":{"id":"2503.20456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-26T11:37:55Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"18094221cd2cea24592f980ca4676b734674c2eabe243e90bbb7fd0b93bc60b9","abstract_canon_sha256":"214927601148e2c61018186cbacf5e617becb1ab49ce81a3be211c39d2890968"},"schema_version":"1.0"},"canonical_sha256":"25f8ababeb482fe0794caf2c433fb8e374be6ce027c4da55be42dd7c573e67df","source":{"kind":"arxiv","id":"2503.20456","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.20456","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"2503.20456v1","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.20456","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"EX4KXK7LJAX6","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"pith_short_16","alias_value":"EX4KXK7LJAX6A6KM","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"pith_short_8","alias_value":"EX4KXK7L","created_at":"2026-07-05T10:39:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EX4KXK7LJAX6A6KMV4WEGP5Y4N","target":"record","payload":{"canonical_record":{"source":{"id":"2503.20456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-26T11:37:55Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"18094221cd2cea24592f980ca4676b734674c2eabe243e90bbb7fd0b93bc60b9","abstract_canon_sha256":"214927601148e2c61018186cbacf5e617becb1ab49ce81a3be211c39d2890968"},"schema_version":"1.0"},"canonical_sha256":"25f8ababeb482fe0794caf2c433fb8e374be6ce027c4da55be42dd7c573e67df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:39:38.743421Z","signature_b64":"cYkxyxJuN9CTiMIlsQLyOY3RuF0e9QQIzCO1kTfBrem2Vx5vCJWBlGGOPK6PpF5vnu/6i5+FHa4UBYRFR/6yCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25f8ababeb482fe0794caf2c433fb8e374be6ce027c4da55be42dd7c573e67df","last_reissued_at":"2026-07-05T10:39:38.742940Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:39:38.742940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.20456","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":"2026-07-05T10:39:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G2K1u9dHR0QSf6IIYJUHr+Ursb10NxWvvbgI1ZDFifkcVAJztx/GRFl/SyXqdWfvifCnAQdicPCO+1qdVgZwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:24:31.492279Z"},"content_sha256":"425adc771225ddc6cff5097fda64c33e8cb0f32b0441556eaab18123fbb6e16b","schema_version":"1.0","event_id":"sha256:425adc771225ddc6cff5097fda64c33e8cb0f32b0441556eaab18123fbb6e16b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EX4KXK7LJAX6A6KMV4WEGP5Y4N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bordism categories and orientations of moduli spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.AT","authors_text":"Dominic Joyce, Markus Upmeier","submitted_at":"2025-03-26T11:37:55Z","abstract_excerpt":"To define enumerative invariants in geometry, one often needs orientations on moduli spaces of geometric objects. This monograph develops a new bordism-theoretic point of view on orientations of moduli spaces. Let $X$ be a manifold with geometric structure, and $\\cal M$ a moduli space of geometric objects on $X$. Our theory aims to answer the questions:\n  (i) Can we prove $\\cal M$ is orientable for all $X,\\cal M$?\n  (ii) If not, can we give computable sufficient conditions on $X$ that guarantee $\\cal M$ is orientable?\n  (iii) Can we specify extra data on $X$ which allow us to construct a canon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.20456","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.20456/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:39:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQCn5TEW4ZzRR6nx9br4WppnJgPm/PCui67GZbRLM75EBSLkGJi8mJLwGvWGFBqtCYMbw8lfpKUQXB2CtkY0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T14:24:31.493186Z"},"content_sha256":"13872252bebfb72342fcc4daabffca4b7e67bb79b152d411157f5186ef350b4c","schema_version":"1.0","event_id":"sha256:13872252bebfb72342fcc4daabffca4b7e67bb79b152d411157f5186ef350b4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EX4KXK7LJAX6A6KMV4WEGP5Y4N/bundle.json","state_url":"https://pith.science/pith/EX4KXK7LJAX6A6KMV4WEGP5Y4N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EX4KXK7LJAX6A6KMV4WEGP5Y4N/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":"2026-08-03T14:24:31Z","links":{"resolver":"https://pith.science/pith/EX4KXK7LJAX6A6KMV4WEGP5Y4N","bundle":"https://pith.science/pith/EX4KXK7LJAX6A6KMV4WEGP5Y4N/bundle.json","state":"https://pith.science/pith/EX4KXK7LJAX6A6KMV4WEGP5Y4N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EX4KXK7LJAX6A6KMV4WEGP5Y4N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EX4KXK7LJAX6A6KMV4WEGP5Y4N","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":"214927601148e2c61018186cbacf5e617becb1ab49ce81a3be211c39d2890968","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-26T11:37:55Z","title_canon_sha256":"18094221cd2cea24592f980ca4676b734674c2eabe243e90bbb7fd0b93bc60b9"},"schema_version":"1.0","source":{"id":"2503.20456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.20456","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"2503.20456v1","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.20456","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"EX4KXK7LJAX6","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"pith_short_16","alias_value":"EX4KXK7LJAX6A6KM","created_at":"2026-07-05T10:39:38Z"},{"alias_kind":"pith_short_8","alias_value":"EX4KXK7L","created_at":"2026-07-05T10:39:38Z"}],"graph_snapshots":[{"event_id":"sha256:13872252bebfb72342fcc4daabffca4b7e67bb79b152d411157f5186ef350b4c","target":"graph","created_at":"2026-07-05T10:39:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.20456/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"To define enumerative invariants in geometry, one often needs orientations on moduli spaces of geometric objects. This monograph develops a new bordism-theoretic point of view on orientations of moduli spaces. Let $X$ be a manifold with geometric structure, and $\\cal M$ a moduli space of geometric objects on $X$. Our theory aims to answer the questions:\n  (i) Can we prove $\\cal M$ is orientable for all $X,\\cal M$?\n  (ii) If not, can we give computable sufficient conditions on $X$ that guarantee $\\cal M$ is orientable?\n  (iii) Can we specify extra data on $X$ which allow us to construct a canon","authors_text":"Dominic Joyce, Markus Upmeier","cross_cats":["math.AG","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-26T11:37:55Z","title":"Bordism categories and orientations of moduli spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.20456","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":"sha256:425adc771225ddc6cff5097fda64c33e8cb0f32b0441556eaab18123fbb6e16b","target":"record","created_at":"2026-07-05T10:39:38Z","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":"214927601148e2c61018186cbacf5e617becb1ab49ce81a3be211c39d2890968","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-03-26T11:37:55Z","title_canon_sha256":"18094221cd2cea24592f980ca4676b734674c2eabe243e90bbb7fd0b93bc60b9"},"schema_version":"1.0","source":{"id":"2503.20456","kind":"arxiv","version":1}},"canonical_sha256":"25f8ababeb482fe0794caf2c433fb8e374be6ce027c4da55be42dd7c573e67df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25f8ababeb482fe0794caf2c433fb8e374be6ce027c4da55be42dd7c573e67df","first_computed_at":"2026-07-05T10:39:38.742940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:39:38.742940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cYkxyxJuN9CTiMIlsQLyOY3RuF0e9QQIzCO1kTfBrem2Vx5vCJWBlGGOPK6PpF5vnu/6i5+FHa4UBYRFR/6yCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:39:38.743421Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.20456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:425adc771225ddc6cff5097fda64c33e8cb0f32b0441556eaab18123fbb6e16b","sha256:13872252bebfb72342fcc4daabffca4b7e67bb79b152d411157f5186ef350b4c"],"state_sha256":"c49981b366f16eead714c7f3870dba278bbcee383bc26b991a0e987316e2cbb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lcvR0zoTzP6DaGFl1SRfsJGKgZDU8Z5ILv0/687cdhLgxxzibm7zbElUXJf9DDkvefVFHqu02h9zOklvk+YUAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T14:24:31.501450Z","bundle_sha256":"fce6480e5bd9d0ca1d846d7a75fa4a4df3b12f53077c0ed104dce117b2427fcf"}}