{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:P7MRMMLKR3M5PZ7TXJVUEMLCRY","short_pith_number":"pith:P7MRMMLK","canonical_record":{"source":{"id":"2502.01504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-03T16:37:49Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bc2f52f1fcc1c78809a05d668150ea3fe2672dec2c8813d5ca7bdfe7c18c050a","abstract_canon_sha256":"692f689c5c3b172a5bf7eaa1251e03450dc3964ea0ac9922b5c35505f3a029cd"},"schema_version":"1.0"},"canonical_sha256":"7fd916316a8ed9d7e7f3ba6b4231628e097e9bf29851295e342b6b290957c1d6","source":{"kind":"arxiv","id":"2502.01504","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01504","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01504v3","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01504","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"P7MRMMLKR3M5","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_16","alias_value":"P7MRMMLKR3M5PZ7T","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_8","alias_value":"P7MRMMLK","created_at":"2026-06-11T01:10:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:P7MRMMLKR3M5PZ7TXJVUEMLCRY","target":"record","payload":{"canonical_record":{"source":{"id":"2502.01504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-03T16:37:49Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bc2f52f1fcc1c78809a05d668150ea3fe2672dec2c8813d5ca7bdfe7c18c050a","abstract_canon_sha256":"692f689c5c3b172a5bf7eaa1251e03450dc3964ea0ac9922b5c35505f3a029cd"},"schema_version":"1.0"},"canonical_sha256":"7fd916316a8ed9d7e7f3ba6b4231628e097e9bf29851295e342b6b290957c1d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:10:25.273061Z","signature_b64":"u09z4HEeQgTL46nSy/LOTcguPZICPbYwk7R+tiGWZSqOPooM+y5OuJ8iCvn9+avUqCAic87ZmJR6lT6qYludDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fd916316a8ed9d7e7f3ba6b4231628e097e9bf29851295e342b6b290957c1d6","last_reissued_at":"2026-06-11T01:10:25.272366Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:10:25.272366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.01504","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":"2026-06-11T01:10:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCS0qNDZi/UOQQDYbw2x5QLSzSKzs7oIC679A3SKoMpna8DyHgE+2QIHbj0ZEjl+IXSgB/PX1eJGj++5etLaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:16:34.066623Z"},"content_sha256":"70edd972563f7bae4801a150bec456b1b0e86a89fe6f9818a63036394fce105e","schema_version":"1.0","event_id":"sha256:70edd972563f7bae4801a150bec456b1b0e86a89fe6f9818a63036394fce105e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:P7MRMMLKR3M5PZ7TXJVUEMLCRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finiteness of formal pushforwards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Daniel Krashen, David Harbater, Julia Hartmann","submitted_at":"2025-02-03T16:37:49Z","abstract_excerpt":"Under mild hypotheses, given a scheme $U$ and an open subset $V$ whose complement has codimension at least two, the pushforward of a torsion-free coherent sheaf on $V$ is coherent on $U$, and in particular is finite. We prove an analog of this finiteness assertion in the context of formal schemes over a complete discrete valuation ring, but show that coherence does not always hold. We then relate this to the problem of gluing formal functions, where the patches do not cover the entire scheme."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01504","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.01504/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":"2026-06-11T01:10:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SMUHrhdeqU4UQtCr/MKLyNtfAZERo8boWTjFTkauU/2qLjWHG/ZgT6tyHoqz6EuT52khGYqmizyNvzpuiCCTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:16:34.066986Z"},"content_sha256":"314f91ddff30b7585e38e3c3aa71c6fc554a83c2a3dd203cdc5a997e556396bf","schema_version":"1.0","event_id":"sha256:314f91ddff30b7585e38e3c3aa71c6fc554a83c2a3dd203cdc5a997e556396bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7MRMMLKR3M5PZ7TXJVUEMLCRY/bundle.json","state_url":"https://pith.science/pith/P7MRMMLKR3M5PZ7TXJVUEMLCRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7MRMMLKR3M5PZ7TXJVUEMLCRY/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":"2026-06-20T18:16:34Z","links":{"resolver":"https://pith.science/pith/P7MRMMLKR3M5PZ7TXJVUEMLCRY","bundle":"https://pith.science/pith/P7MRMMLKR3M5PZ7TXJVUEMLCRY/bundle.json","state":"https://pith.science/pith/P7MRMMLKR3M5PZ7TXJVUEMLCRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7MRMMLKR3M5PZ7TXJVUEMLCRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:P7MRMMLKR3M5PZ7TXJVUEMLCRY","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":"692f689c5c3b172a5bf7eaa1251e03450dc3964ea0ac9922b5c35505f3a029cd","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-03T16:37:49Z","title_canon_sha256":"bc2f52f1fcc1c78809a05d668150ea3fe2672dec2c8813d5ca7bdfe7c18c050a"},"schema_version":"1.0","source":{"id":"2502.01504","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01504","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01504v3","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01504","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"P7MRMMLKR3M5","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_16","alias_value":"P7MRMMLKR3M5PZ7T","created_at":"2026-06-11T01:10:25Z"},{"alias_kind":"pith_short_8","alias_value":"P7MRMMLK","created_at":"2026-06-11T01:10:25Z"}],"graph_snapshots":[{"event_id":"sha256:314f91ddff30b7585e38e3c3aa71c6fc554a83c2a3dd203cdc5a997e556396bf","target":"graph","created_at":"2026-06-11T01:10:25Z","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/2502.01504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Under mild hypotheses, given a scheme $U$ and an open subset $V$ whose complement has codimension at least two, the pushforward of a torsion-free coherent sheaf on $V$ is coherent on $U$, and in particular is finite. We prove an analog of this finiteness assertion in the context of formal schemes over a complete discrete valuation ring, but show that coherence does not always hold. We then relate this to the problem of gluing formal functions, where the patches do not cover the entire scheme.","authors_text":"Daniel Krashen, David Harbater, Julia Hartmann","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-03T16:37:49Z","title":"Finiteness of formal pushforwards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01504","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":"sha256:70edd972563f7bae4801a150bec456b1b0e86a89fe6f9818a63036394fce105e","target":"record","created_at":"2026-06-11T01:10:25Z","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":"692f689c5c3b172a5bf7eaa1251e03450dc3964ea0ac9922b5c35505f3a029cd","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-03T16:37:49Z","title_canon_sha256":"bc2f52f1fcc1c78809a05d668150ea3fe2672dec2c8813d5ca7bdfe7c18c050a"},"schema_version":"1.0","source":{"id":"2502.01504","kind":"arxiv","version":3}},"canonical_sha256":"7fd916316a8ed9d7e7f3ba6b4231628e097e9bf29851295e342b6b290957c1d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fd916316a8ed9d7e7f3ba6b4231628e097e9bf29851295e342b6b290957c1d6","first_computed_at":"2026-06-11T01:10:25.272366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:25.272366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u09z4HEeQgTL46nSy/LOTcguPZICPbYwk7R+tiGWZSqOPooM+y5OuJ8iCvn9+avUqCAic87ZmJR6lT6qYludDQ==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:25.273061Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.01504","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70edd972563f7bae4801a150bec456b1b0e86a89fe6f9818a63036394fce105e","sha256:314f91ddff30b7585e38e3c3aa71c6fc554a83c2a3dd203cdc5a997e556396bf"],"state_sha256":"5e9b223a24fa527a9a7b73380cbf1eba608e9292285f8de510679b366b3915fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lMCqchd/D6sHM0vo4pKaR++gsrkJq6h7SRr0kABT0It8R/6uRBY89uAyUtI8aouOGJqtkKWf0/6lMsQBX24GAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:16:34.068940Z","bundle_sha256":"a453ac98762cfbc4899d128566fec4ec3ed23a57ad9656922f9984e9b0ed0d88"}}