{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CQZCNNZ7YFTF3NXHK4RC4VMPB6","short_pith_number":"pith:CQZCNNZ7","canonical_record":{"source":{"id":"1712.05971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-16T15:02:40Z","cross_cats_sorted":["math-ph","math.AG","math.AT","math.MP"],"title_canon_sha256":"857a6e403a3d9ca975e4cabd48c5783b24ed15f76f01053d423d44a1abad6d5b","abstract_canon_sha256":"bcab1da4e5feefb8b04526f4f5815ccf27527ec0d662ecee1782886f16557363"},"schema_version":"1.0"},"canonical_sha256":"143226b73fc1665db6e757222e558f0fba5bd6b454f138bbcc5922e3f2fb0da7","source":{"kind":"arxiv","id":"1712.05971","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05971","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05971v2","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05971","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"CQZCNNZ7YFTF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CQZCNNZ7YFTF3NXH","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CQZCNNZ7","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CQZCNNZ7YFTF3NXHK4RC4VMPB6","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-16T15:02:40Z","cross_cats_sorted":["math-ph","math.AG","math.AT","math.MP"],"title_canon_sha256":"857a6e403a3d9ca975e4cabd48c5783b24ed15f76f01053d423d44a1abad6d5b","abstract_canon_sha256":"bcab1da4e5feefb8b04526f4f5815ccf27527ec0d662ecee1782886f16557363"},"schema_version":"1.0"},"canonical_sha256":"143226b73fc1665db6e757222e558f0fba5bd6b454f138bbcc5922e3f2fb0da7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:51.057722Z","signature_b64":"F1CdXmq4JOw674xnZDV6pZ+CvWVyvpykhc2NlVlHoPPhb6PyfvAbys82HnVLZayb3VCRy6cZlnA6Kg8SxJgHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"143226b73fc1665db6e757222e558f0fba5bd6b454f138bbcc5922e3f2fb0da7","last_reissued_at":"2026-05-18T00:05:51.057090Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:51.057090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05971","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+VjOVUkxW7yKduR8/OEbO9p6MwKKrpqXlJJcqen8YHq/ydKZafsfjFE3eJfXXX4ONTLvkqbeFUUm8xiXSgAxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T10:46:50.672487Z"},"content_sha256":"c02e56cfc101c404cb580ad9a8d5aee8c5dcf1c90f8171025204bb3684c21d16","schema_version":"1.0","event_id":"sha256:c02e56cfc101c404cb580ad9a8d5aee8c5dcf1c90f8171025204bb3684c21d16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CQZCNNZ7YFTF3NXHK4RC4VMPB6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-twisted periodic smooth Deligne cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.AT","math.MP"],"primary_cat":"math.DG","authors_text":"Daniel Grady, Hisham Sati","submitted_at":"2017-12-16T15:02:40Z","abstract_excerpt":"Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a periodic version. Combining the periodic versions of both ingredients leads us to introduce a periodic form of Deligne cohomology. We demonstrate that this theory indeed admits a twist by a gerbe of any odd degree. We present the main properties of the new theory and illustrate its u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05971","kind":"arxiv","version":2},"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":"2026-05-18T00:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sgwi6nSb6Srfe2PYGkZrMrmZnMlAEY+fwr+G7cev4dkQnldcPd9KhS07Rwv8psUoDkxW+4DRiPtRmsBMkBwQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T10:46:50.672962Z"},"content_sha256":"893ef53cee20c82bcecf1271b090b1085a15506873975bb70ba156b207128d90","schema_version":"1.0","event_id":"sha256:893ef53cee20c82bcecf1271b090b1085a15506873975bb70ba156b207128d90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQZCNNZ7YFTF3NXHK4RC4VMPB6/bundle.json","state_url":"https://pith.science/pith/CQZCNNZ7YFTF3NXHK4RC4VMPB6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQZCNNZ7YFTF3NXHK4RC4VMPB6/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":"2026-08-15T10:46:50Z","links":{"resolver":"https://pith.science/pith/CQZCNNZ7YFTF3NXHK4RC4VMPB6","bundle":"https://pith.science/pith/CQZCNNZ7YFTF3NXHK4RC4VMPB6/bundle.json","state":"https://pith.science/pith/CQZCNNZ7YFTF3NXHK4RC4VMPB6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQZCNNZ7YFTF3NXHK4RC4VMPB6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CQZCNNZ7YFTF3NXHK4RC4VMPB6","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":"bcab1da4e5feefb8b04526f4f5815ccf27527ec0d662ecee1782886f16557363","cross_cats_sorted":["math-ph","math.AG","math.AT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-16T15:02:40Z","title_canon_sha256":"857a6e403a3d9ca975e4cabd48c5783b24ed15f76f01053d423d44a1abad6d5b"},"schema_version":"1.0","source":{"id":"1712.05971","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05971","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05971v2","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05971","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"CQZCNNZ7YFTF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CQZCNNZ7YFTF3NXH","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CQZCNNZ7","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:893ef53cee20c82bcecf1271b090b1085a15506873975bb70ba156b207128d90","target":"graph","created_at":"2026-05-18T00:05:51Z","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":"Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a periodic version. Combining the periodic versions of both ingredients leads us to introduce a periodic form of Deligne cohomology. We demonstrate that this theory indeed admits a twist by a gerbe of any odd degree. We present the main properties of the new theory and illustrate its u","authors_text":"Daniel Grady, Hisham Sati","cross_cats":["math-ph","math.AG","math.AT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-16T15:02:40Z","title":"Higher-twisted periodic smooth Deligne cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05971","kind":"arxiv","version":2},"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:c02e56cfc101c404cb580ad9a8d5aee8c5dcf1c90f8171025204bb3684c21d16","target":"record","created_at":"2026-05-18T00:05:51Z","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":"bcab1da4e5feefb8b04526f4f5815ccf27527ec0d662ecee1782886f16557363","cross_cats_sorted":["math-ph","math.AG","math.AT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-16T15:02:40Z","title_canon_sha256":"857a6e403a3d9ca975e4cabd48c5783b24ed15f76f01053d423d44a1abad6d5b"},"schema_version":"1.0","source":{"id":"1712.05971","kind":"arxiv","version":2}},"canonical_sha256":"143226b73fc1665db6e757222e558f0fba5bd6b454f138bbcc5922e3f2fb0da7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"143226b73fc1665db6e757222e558f0fba5bd6b454f138bbcc5922e3f2fb0da7","first_computed_at":"2026-05-18T00:05:51.057090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:51.057090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F1CdXmq4JOw674xnZDV6pZ+CvWVyvpykhc2NlVlHoPPhb6PyfvAbys82HnVLZayb3VCRy6cZlnA6Kg8SxJgHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:51.057722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05971","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c02e56cfc101c404cb580ad9a8d5aee8c5dcf1c90f8171025204bb3684c21d16","sha256:893ef53cee20c82bcecf1271b090b1085a15506873975bb70ba156b207128d90"],"state_sha256":"b9ad380576a57d4caf7047883461da83eccd6ba748c616ac70c0493cd45c9ae9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CHBKWTPLheOkeWluKV/MomlXD4Bp0zwyejYtAfN0bwgtz7PyTWdh4SAGKiKPgRDiZHEq3xSZpEUGK2ZcnCPDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T10:46:50.678321Z","bundle_sha256":"50988b7be41e99ef07bf6f93e1cf6672edd40465fc5652253c6ed675fd5f021d"}}