{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JGI2XY6CHYHUK66NFLQ7G7Y6BB","short_pith_number":"pith:JGI2XY6C","canonical_record":{"source":{"id":"1707.07480","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T11:05:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"724ebc9fba3fdd9307065cbfe9f0ac269d968785aec7dcf632e131d836c61633","abstract_canon_sha256":"fd2355628435a66d1d56cd44a04981d5547b0d1c7c141234e8de7cfa5271160f"},"schema_version":"1.0"},"canonical_sha256":"4991abe3c23e0f457bcd2ae1f37f1e0868769d3758a5d4c972292b46480740ab","source":{"kind":"arxiv","id":"1707.07480","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07480","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07480v4","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07480","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"pith_short_12","alias_value":"JGI2XY6CHYHU","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JGI2XY6CHYHUK66N","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JGI2XY6C","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JGI2XY6CHYHUK66NFLQ7G7Y6BB","target":"record","payload":{"canonical_record":{"source":{"id":"1707.07480","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T11:05:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"724ebc9fba3fdd9307065cbfe9f0ac269d968785aec7dcf632e131d836c61633","abstract_canon_sha256":"fd2355628435a66d1d56cd44a04981d5547b0d1c7c141234e8de7cfa5271160f"},"schema_version":"1.0"},"canonical_sha256":"4991abe3c23e0f457bcd2ae1f37f1e0868769d3758a5d4c972292b46480740ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:19.044095Z","signature_b64":"EHVX0hTTWRx4uMo4HTJn+bsPZlLNUiDYRUkcVEhSPYYwq9gkBQRshcUs7BVv58y3mzgrhswNoi1Jko+MTzsZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4991abe3c23e0f457bcd2ae1f37f1e0868769d3758a5d4c972292b46480740ab","last_reissued_at":"2026-05-18T00:36:19.043446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:19.043446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.07480","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K0YJWeOTXO5RmSg9n+yrB2UR0wEON2gxQsBY1xeO4EHYcdebzqF/udB7hsN/w8tQcDj+43vCng7nEqz71DXcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:57:12.183469Z"},"content_sha256":"a3b981164e7c0b7f94ecdeeaa7fa26464e4b171e39dc7ac97721921e54e79227","schema_version":"1.0","event_id":"sha256:a3b981164e7c0b7f94ecdeeaa7fa26464e4b171e39dc7ac97721921e54e79227"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JGI2XY6CHYHUK66NFLQ7G7Y6BB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformations of abstract Brieskorn lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Morihiko Saito","submitted_at":"2017-07-24T11:05:31Z","abstract_excerpt":"We study certain deformations of abstract Brieskorn lattices in fixed abstract Gauss-Manin systems, and show that the ambiguity of expressions of deformations coming from automorphisms of base spaces is essentially the same as the one coming from the choice of opposite filtrations, and hence is finite dimensional, although the freedom of parameters in the expressions of deformations is infinite dimensional. As a consequence, we can prove the non-existence of a versal deformation of the Fourier transform of this abstract Brieskorn lattice with expected dimension. This shows that the generation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07480","kind":"arxiv","version":4},"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":"2026-05-18T00:36:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODbUEA8YqJ6znKOv4ameO0S6egOJrZKqIduqMhHBuo2RC+xAw27TXrsrH14teWo92pkp8Evjaf1v9Fwf0Vv6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:57:12.184214Z"},"content_sha256":"7d2c17d19c984ea5bb9d689c41b28e00f7f6b22aefc9060f82c44e65315a28f3","schema_version":"1.0","event_id":"sha256:7d2c17d19c984ea5bb9d689c41b28e00f7f6b22aefc9060f82c44e65315a28f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JGI2XY6CHYHUK66NFLQ7G7Y6BB/bundle.json","state_url":"https://pith.science/pith/JGI2XY6CHYHUK66NFLQ7G7Y6BB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JGI2XY6CHYHUK66NFLQ7G7Y6BB/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":"2026-06-11T15:57:12Z","links":{"resolver":"https://pith.science/pith/JGI2XY6CHYHUK66NFLQ7G7Y6BB","bundle":"https://pith.science/pith/JGI2XY6CHYHUK66NFLQ7G7Y6BB/bundle.json","state":"https://pith.science/pith/JGI2XY6CHYHUK66NFLQ7G7Y6BB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JGI2XY6CHYHUK66NFLQ7G7Y6BB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JGI2XY6CHYHUK66NFLQ7G7Y6BB","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":"fd2355628435a66d1d56cd44a04981d5547b0d1c7c141234e8de7cfa5271160f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T11:05:31Z","title_canon_sha256":"724ebc9fba3fdd9307065cbfe9f0ac269d968785aec7dcf632e131d836c61633"},"schema_version":"1.0","source":{"id":"1707.07480","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07480","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07480v4","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07480","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"pith_short_12","alias_value":"JGI2XY6CHYHU","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JGI2XY6CHYHUK66N","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JGI2XY6C","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:7d2c17d19c984ea5bb9d689c41b28e00f7f6b22aefc9060f82c44e65315a28f3","target":"graph","created_at":"2026-05-18T00:36:19Z","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 study certain deformations of abstract Brieskorn lattices in fixed abstract Gauss-Manin systems, and show that the ambiguity of expressions of deformations coming from automorphisms of base spaces is essentially the same as the one coming from the choice of opposite filtrations, and hence is finite dimensional, although the freedom of parameters in the expressions of deformations is infinite dimensional. As a consequence, we can prove the non-existence of a versal deformation of the Fourier transform of this abstract Brieskorn lattice with expected dimension. This shows that the generation ","authors_text":"Morihiko Saito","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T11:05:31Z","title":"Deformations of abstract Brieskorn lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07480","kind":"arxiv","version":4},"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:a3b981164e7c0b7f94ecdeeaa7fa26464e4b171e39dc7ac97721921e54e79227","target":"record","created_at":"2026-05-18T00:36:19Z","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":"fd2355628435a66d1d56cd44a04981d5547b0d1c7c141234e8de7cfa5271160f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-24T11:05:31Z","title_canon_sha256":"724ebc9fba3fdd9307065cbfe9f0ac269d968785aec7dcf632e131d836c61633"},"schema_version":"1.0","source":{"id":"1707.07480","kind":"arxiv","version":4}},"canonical_sha256":"4991abe3c23e0f457bcd2ae1f37f1e0868769d3758a5d4c972292b46480740ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4991abe3c23e0f457bcd2ae1f37f1e0868769d3758a5d4c972292b46480740ab","first_computed_at":"2026-05-18T00:36:19.043446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:19.043446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EHVX0hTTWRx4uMo4HTJn+bsPZlLNUiDYRUkcVEhSPYYwq9gkBQRshcUs7BVv58y3mzgrhswNoi1Jko+MTzsZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:19.044095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07480","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3b981164e7c0b7f94ecdeeaa7fa26464e4b171e39dc7ac97721921e54e79227","sha256:7d2c17d19c984ea5bb9d689c41b28e00f7f6b22aefc9060f82c44e65315a28f3"],"state_sha256":"5e837d7ea25a195e360b945ed90a82a18aa65a9e4a152c6dd0166700493fe56c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lt2kDOizQqSET52g9k8FT0r8G1wrbkGuwS4KIRzoy1JTlUlSttHSu/fLLzxI2I46t5ykwHZzcQyrUVLmY1neAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:57:12.188696Z","bundle_sha256":"050e2099c5a7fbceca937ad54a3d0e4e7ede6dc0bb9901bd4ab6f68e026bb47d"}}