{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LXJRQCHA7MWB4YZCSYGLJKLAGK","short_pith_number":"pith:LXJRQCHA","canonical_record":{"source":{"id":"1510.06366","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-10-21T18:48:41Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"0b87efd368ef6cea10e0127d5a67059d6c1a5fd07690a7594a3533579b07993b","abstract_canon_sha256":"b2712278bc1d827ffdf210079e3621ab61ba9e6f7e1e73ec9ebd8d9ee8e8f312"},"schema_version":"1.0"},"canonical_sha256":"5dd31808e0fb2c1e6322960cb4a96032b52577349b190884209e6377aaadd1c9","source":{"kind":"arxiv","id":"1510.06366","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06366","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06366v3","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06366","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"LXJRQCHA7MWB","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXJRQCHA7MWB4YZC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXJRQCHA","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LXJRQCHA7MWB4YZCSYGLJKLAGK","target":"record","payload":{"canonical_record":{"source":{"id":"1510.06366","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-10-21T18:48:41Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"0b87efd368ef6cea10e0127d5a67059d6c1a5fd07690a7594a3533579b07993b","abstract_canon_sha256":"b2712278bc1d827ffdf210079e3621ab61ba9e6f7e1e73ec9ebd8d9ee8e8f312"},"schema_version":"1.0"},"canonical_sha256":"5dd31808e0fb2c1e6322960cb4a96032b52577349b190884209e6377aaadd1c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:06.939471Z","signature_b64":"fK6X0syU4HgZS8IbmlFciSf0Gr5ML0+n/+F5hpescphZ6WZr/PqCME8WhsZhYFc40SubOEEDN1zdjqtmmdgvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dd31808e0fb2c1e6322960cb4a96032b52577349b190884209e6377aaadd1c9","last_reissued_at":"2026-05-18T00:22:06.939052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:06.939052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.06366","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0XE3sWOhHSe3J2XViZ9CliwVsO+46gM/aiirnG3mhiPMnH5KsZRsAdysWJY6yFbI8QRpV1xW9oZD6Dp5nSPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:11:45.788654Z"},"content_sha256":"3bbc62b122b7217b7cf2453800ba07210ad8a11165640732b8edd480ec4a41a6","schema_version":"1.0","event_id":"sha256:3bbc62b122b7217b7cf2453800ba07210ad8a11165640732b8edd480ec4a41a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LXJRQCHA7MWB4YZCSYGLJKLAGK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Massey products in differential cohomology via stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.AT","authors_text":"Daniel Grady, Hisham Sati","submitted_at":"2015-10-21T18:48:41Z","abstract_excerpt":"We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties and show how they are related to more classical Massey products in de Rham, singular, and Deligne cohomology. The setting and the algebraic machinery via stacks allow for computations and make the construction well-suited for applications. We illustrate with several examples from differential geometry and mathematical physics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06366","kind":"arxiv","version":3},"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":"2026-05-18T00:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B9OsCPHJDqcjdxHMAKSsK8/NZFL5CnWG+OGyh02OfNmYQ5x+evdjS4kFJOfaEcz01E8tOoENxRklnTSJJMIDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:11:45.788995Z"},"content_sha256":"7a46c9b82b3389487077cc905f05718e914056b7faf9519b363fa9e0b3978694","schema_version":"1.0","event_id":"sha256:7a46c9b82b3389487077cc905f05718e914056b7faf9519b363fa9e0b3978694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXJRQCHA7MWB4YZCSYGLJKLAGK/bundle.json","state_url":"https://pith.science/pith/LXJRQCHA7MWB4YZCSYGLJKLAGK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXJRQCHA7MWB4YZCSYGLJKLAGK/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":"2026-06-12T10:11:45Z","links":{"resolver":"https://pith.science/pith/LXJRQCHA7MWB4YZCSYGLJKLAGK","bundle":"https://pith.science/pith/LXJRQCHA7MWB4YZCSYGLJKLAGK/bundle.json","state":"https://pith.science/pith/LXJRQCHA7MWB4YZCSYGLJKLAGK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXJRQCHA7MWB4YZCSYGLJKLAGK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LXJRQCHA7MWB4YZCSYGLJKLAGK","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":"b2712278bc1d827ffdf210079e3621ab61ba9e6f7e1e73ec9ebd8d9ee8e8f312","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-10-21T18:48:41Z","title_canon_sha256":"0b87efd368ef6cea10e0127d5a67059d6c1a5fd07690a7594a3533579b07993b"},"schema_version":"1.0","source":{"id":"1510.06366","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06366","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06366v3","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06366","created_at":"2026-05-18T00:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"LXJRQCHA7MWB","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LXJRQCHA7MWB4YZC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LXJRQCHA","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:7a46c9b82b3389487077cc905f05718e914056b7faf9519b363fa9e0b3978694","target":"graph","created_at":"2026-05-18T00:22:06Z","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 extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties and show how they are related to more classical Massey products in de Rham, singular, and Deligne cohomology. The setting and the algebraic machinery via stacks allow for computations and make the construction well-suited for applications. We illustrate with several examples from differential geometry and mathematical physics.","authors_text":"Daniel Grady, Hisham Sati","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-10-21T18:48:41Z","title":"Massey products in differential cohomology via stacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06366","kind":"arxiv","version":3},"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":"sha256:3bbc62b122b7217b7cf2453800ba07210ad8a11165640732b8edd480ec4a41a6","target":"record","created_at":"2026-05-18T00:22:06Z","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":"b2712278bc1d827ffdf210079e3621ab61ba9e6f7e1e73ec9ebd8d9ee8e8f312","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-10-21T18:48:41Z","title_canon_sha256":"0b87efd368ef6cea10e0127d5a67059d6c1a5fd07690a7594a3533579b07993b"},"schema_version":"1.0","source":{"id":"1510.06366","kind":"arxiv","version":3}},"canonical_sha256":"5dd31808e0fb2c1e6322960cb4a96032b52577349b190884209e6377aaadd1c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dd31808e0fb2c1e6322960cb4a96032b52577349b190884209e6377aaadd1c9","first_computed_at":"2026-05-18T00:22:06.939052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:06.939052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fK6X0syU4HgZS8IbmlFciSf0Gr5ML0+n/+F5hpescphZ6WZr/PqCME8WhsZhYFc40SubOEEDN1zdjqtmmdgvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:06.939471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06366","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bbc62b122b7217b7cf2453800ba07210ad8a11165640732b8edd480ec4a41a6","sha256:7a46c9b82b3389487077cc905f05718e914056b7faf9519b363fa9e0b3978694"],"state_sha256":"09f08cb4567dd53612bb38160bcf00f5b9ce0ae99966104465599f34273eb926"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iu2WVZPGDiAmHAkAeX9sI0jkuu0136ePZO8UpktvIxgQ41zia9UvypKlwFKby4dzc2s0BFWhufk4ARUaeU/cCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:11:45.790937Z","bundle_sha256":"eb294fd237111df9ac7c2634c4564f9ad2f4bda4b473ce624bcfffb48d99c5e6"}}