{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DFMMGXHUGU7JOUXON2DD24RMHD","short_pith_number":"pith:DFMMGXHU","canonical_record":{"source":{"id":"1112.4173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-18T17:51:18Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"d9259b47cc0cff9e289a9abaa61ae8a2d061f265afa9ec927cc4c1f64ecd3da2","abstract_canon_sha256":"3c6e7f188eef8abbbb11ee9b07f81ba1b0939e6db25161ed3a2b90e04baea1b6"},"schema_version":"1.0"},"canonical_sha256":"1958c35cf4353e9752ee6e863d722c38d984bb2d98505256979c03e627fd93e1","source":{"kind":"arxiv","id":"1112.4173","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4173","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4173v2","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4173","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"DFMMGXHUGU7J","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DFMMGXHUGU7JOUXO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DFMMGXHU","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DFMMGXHUGU7JOUXON2DD24RMHD","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-18T17:51:18Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"d9259b47cc0cff9e289a9abaa61ae8a2d061f265afa9ec927cc4c1f64ecd3da2","abstract_canon_sha256":"3c6e7f188eef8abbbb11ee9b07f81ba1b0939e6db25161ed3a2b90e04baea1b6"},"schema_version":"1.0"},"canonical_sha256":"1958c35cf4353e9752ee6e863d722c38d984bb2d98505256979c03e627fd93e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:45.061224Z","signature_b64":"FmF1SzVevKvhnvQ5hjzBqBodCX0ayXxfAAWqT/4soQ/YicxCn5GLeOEEi5y93NgXM3Wz43H8SjAllFxQ87BzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1958c35cf4353e9752ee6e863d722c38d984bb2d98505256979c03e627fd93e1","last_reissued_at":"2026-05-18T03:48:45.060531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:45.060531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4173","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":"2026-05-18T03:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FeUL2i3I2azZ0oTr/lR7wZ9zm2eXH87PvBsF6nKbfO4WyaI4CwEHxmnhpEu7y+GfOd4PyouENemlJ5k8MHX9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:16:09.894670Z"},"content_sha256":"bf841cf7feaf91ab2bb5375a8ce8305dfdf037123a3617ad99338a8c92438015","schema_version":"1.0","event_id":"sha256:bf841cf7feaf91ab2bb5375a8ce8305dfdf037123a3617ad99338a8c92438015"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DFMMGXHUGU7JOUXON2DD24RMHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Products in Generalized Differential Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.GT","authors_text":"Markus Upmeier","submitted_at":"2011-12-18T17:51:18Z","abstract_excerpt":"In this paper it is shown that multiplicative cohomology theories that are rationally even -- a technical condition that is often satisfied -- the Hopkins-Singer construction of generalized differential cohomology has a unital, graded commutative multiplicative structure. To this end, an explicit integration and a differential cohomology theory for pairs are also developed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4173","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":"2026-05-18T03:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CnOAcXFnSyPg2fGPI3GwJPRd3aTbvm7nGMssmM+Fv6LGfvTDmGFHozOR6EE5tZKEYhzvsvPOPhZM7B/I4eQxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:16:09.895005Z"},"content_sha256":"59071d4c337ac416365897e0a3f7a815eba51629470b94565cd63705061ca9ee","schema_version":"1.0","event_id":"sha256:59071d4c337ac416365897e0a3f7a815eba51629470b94565cd63705061ca9ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFMMGXHUGU7JOUXON2DD24RMHD/bundle.json","state_url":"https://pith.science/pith/DFMMGXHUGU7JOUXON2DD24RMHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFMMGXHUGU7JOUXON2DD24RMHD/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":"2026-06-03T02:16:09Z","links":{"resolver":"https://pith.science/pith/DFMMGXHUGU7JOUXON2DD24RMHD","bundle":"https://pith.science/pith/DFMMGXHUGU7JOUXON2DD24RMHD/bundle.json","state":"https://pith.science/pith/DFMMGXHUGU7JOUXON2DD24RMHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFMMGXHUGU7JOUXON2DD24RMHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DFMMGXHUGU7JOUXON2DD24RMHD","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":"3c6e7f188eef8abbbb11ee9b07f81ba1b0939e6db25161ed3a2b90e04baea1b6","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-18T17:51:18Z","title_canon_sha256":"d9259b47cc0cff9e289a9abaa61ae8a2d061f265afa9ec927cc4c1f64ecd3da2"},"schema_version":"1.0","source":{"id":"1112.4173","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4173","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4173v2","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4173","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"DFMMGXHUGU7J","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DFMMGXHUGU7JOUXO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DFMMGXHU","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:59071d4c337ac416365897e0a3f7a815eba51629470b94565cd63705061ca9ee","target":"graph","created_at":"2026-05-18T03:48:45Z","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":"In this paper it is shown that multiplicative cohomology theories that are rationally even -- a technical condition that is often satisfied -- the Hopkins-Singer construction of generalized differential cohomology has a unital, graded commutative multiplicative structure. To this end, an explicit integration and a differential cohomology theory for pairs are also developed.","authors_text":"Markus Upmeier","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-18T17:51:18Z","title":"Products in Generalized Differential Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4173","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:bf841cf7feaf91ab2bb5375a8ce8305dfdf037123a3617ad99338a8c92438015","target":"record","created_at":"2026-05-18T03:48:45Z","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":"3c6e7f188eef8abbbb11ee9b07f81ba1b0939e6db25161ed3a2b90e04baea1b6","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-12-18T17:51:18Z","title_canon_sha256":"d9259b47cc0cff9e289a9abaa61ae8a2d061f265afa9ec927cc4c1f64ecd3da2"},"schema_version":"1.0","source":{"id":"1112.4173","kind":"arxiv","version":2}},"canonical_sha256":"1958c35cf4353e9752ee6e863d722c38d984bb2d98505256979c03e627fd93e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1958c35cf4353e9752ee6e863d722c38d984bb2d98505256979c03e627fd93e1","first_computed_at":"2026-05-18T03:48:45.060531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:45.060531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FmF1SzVevKvhnvQ5hjzBqBodCX0ayXxfAAWqT/4soQ/YicxCn5GLeOEEi5y93NgXM3Wz43H8SjAllFxQ87BzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:45.061224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4173","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf841cf7feaf91ab2bb5375a8ce8305dfdf037123a3617ad99338a8c92438015","sha256:59071d4c337ac416365897e0a3f7a815eba51629470b94565cd63705061ca9ee"],"state_sha256":"cb487b1b7e3761fc184d1e5c50e6f1e1af642b88a7fc18b588fed4b6101d1354"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4G922w97VW5nlLWSQODfNCrq6tGu/ZDlG4dJnC/QisukJQDXpL4pIjVXDnZ/S9N0vQBJ3etHgRsQabtjzcSPDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:16:09.896875Z","bundle_sha256":"da7d8094f84816cf16e3248bcde8cee37de02c1ae67012b5c70f78916c91ecea"}}