{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FJC2CQ3VHZOP33D73KY24FHJNU","short_pith_number":"pith:FJC2CQ3V","canonical_record":{"source":{"id":"2211.14368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-25T20:37:35Z","cross_cats_sorted":[],"title_canon_sha256":"0ce2326dfaaa3b719ef7bacf8cb3e1fdec05c749dc2c837d834900755d3ea6b0","abstract_canon_sha256":"2be1a76784839791304eaabee6d1299e532e1e228cddc256e6df37ad3973d62c"},"schema_version":"1.0"},"canonical_sha256":"2a45a143753e5cfdec7fdab1ae14e96d002cc76ecc6e6ec605cb1dfb5778f635","source":{"kind":"arxiv","id":"2211.14368","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.14368","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"2211.14368v2","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.14368","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"FJC2CQ3VHZOP","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"pith_short_16","alias_value":"FJC2CQ3VHZOP33D7","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"pith_short_8","alias_value":"FJC2CQ3V","created_at":"2026-07-05T06:48:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FJC2CQ3VHZOP33D73KY24FHJNU","target":"record","payload":{"canonical_record":{"source":{"id":"2211.14368","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-25T20:37:35Z","cross_cats_sorted":[],"title_canon_sha256":"0ce2326dfaaa3b719ef7bacf8cb3e1fdec05c749dc2c837d834900755d3ea6b0","abstract_canon_sha256":"2be1a76784839791304eaabee6d1299e532e1e228cddc256e6df37ad3973d62c"},"schema_version":"1.0"},"canonical_sha256":"2a45a143753e5cfdec7fdab1ae14e96d002cc76ecc6e6ec605cb1dfb5778f635","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:48:46.291184Z","signature_b64":"mWy1BjHOGxTHjrURFoG+h1UnAPYQtd9qzt7KC59bEg9etyGz6nUXZFnrSsckTnAul2Td6Cti/AB2Pudg8tgmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a45a143753e5cfdec7fdab1ae14e96d002cc76ecc6e6ec605cb1dfb5778f635","last_reissued_at":"2026-07-05T06:48:46.290699Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:48:46.290699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.14368","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":"2026-07-05T06:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d7cFZnpZQRrNE4fHGmchm8JflzNAU2Hx+mFdPtwLP/1wCdV6v21TEPQJUgIKkAX9Hsxu73/WweG3OtETrPkeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T16:25:10.664152Z"},"content_sha256":"9be3efda0c12bf3cc966ad2222a28f27a2a4a8e61aaabbd83d52a6bf6fd56ec2","schema_version":"1.0","event_id":"sha256:9be3efda0c12bf3cc966ad2222a28f27a2a4a8e61aaabbd83d52a6bf6fd56ec2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FJC2CQ3VHZOP33D73KY24FHJNU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alberto Casta\\~no Dom\\'inguez, Luis Narv\\'aez Macarro","submitted_at":"2022-11-25T20:37:35Z","abstract_excerpt":"Given two holomorphic functions $f$ and $g$ defined in two respective germs of complex analytic manifolds $(X,x)$ and $(Y,y)$, we know thanks to M. Saito that, as long as one of them is Euler homogeneous, the reduced (or microlocal) Bernstein-Sato polynomial of the Thom-Sebastiani sum $f+g$ can be expressed in terms of those of $f$ and $g$. In this note we give a purely algebraic proof of a similar relation between the whole functional equations that can be applied to any setting (not necessarily analytic) in which Bernstein-Sato polynomials can be defined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.14368","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.14368/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":"2026-07-05T06:48:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NydsHNBPH3t/tzcpAYY+2r1XsRoTVH7NOxmOIHcIHVsY0WVgGjzg7zf2Hksk/Dxhg/0fwlnMsIeR3oYxqCzSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T16:25:10.664561Z"},"content_sha256":"17fe6a73db055a65e5c180b8855b005b5346b02b207fb909c8a80c22fe2bc3fe","schema_version":"1.0","event_id":"sha256:17fe6a73db055a65e5c180b8855b005b5346b02b207fb909c8a80c22fe2bc3fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FJC2CQ3VHZOP33D73KY24FHJNU/bundle.json","state_url":"https://pith.science/pith/FJC2CQ3VHZOP33D73KY24FHJNU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FJC2CQ3VHZOP33D73KY24FHJNU/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":"2026-07-06T16:25:10Z","links":{"resolver":"https://pith.science/pith/FJC2CQ3VHZOP33D73KY24FHJNU","bundle":"https://pith.science/pith/FJC2CQ3VHZOP33D73KY24FHJNU/bundle.json","state":"https://pith.science/pith/FJC2CQ3VHZOP33D73KY24FHJNU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FJC2CQ3VHZOP33D73KY24FHJNU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FJC2CQ3VHZOP33D73KY24FHJNU","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":"2be1a76784839791304eaabee6d1299e532e1e228cddc256e6df37ad3973d62c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-25T20:37:35Z","title_canon_sha256":"0ce2326dfaaa3b719ef7bacf8cb3e1fdec05c749dc2c837d834900755d3ea6b0"},"schema_version":"1.0","source":{"id":"2211.14368","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.14368","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"arxiv_version","alias_value":"2211.14368v2","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.14368","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"pith_short_12","alias_value":"FJC2CQ3VHZOP","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"pith_short_16","alias_value":"FJC2CQ3VHZOP33D7","created_at":"2026-07-05T06:48:46Z"},{"alias_kind":"pith_short_8","alias_value":"FJC2CQ3V","created_at":"2026-07-05T06:48:46Z"}],"graph_snapshots":[{"event_id":"sha256:17fe6a73db055a65e5c180b8855b005b5346b02b207fb909c8a80c22fe2bc3fe","target":"graph","created_at":"2026-07-05T06:48:46Z","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/2211.14368/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given two holomorphic functions $f$ and $g$ defined in two respective germs of complex analytic manifolds $(X,x)$ and $(Y,y)$, we know thanks to M. Saito that, as long as one of them is Euler homogeneous, the reduced (or microlocal) Bernstein-Sato polynomial of the Thom-Sebastiani sum $f+g$ can be expressed in terms of those of $f$ and $g$. In this note we give a purely algebraic proof of a similar relation between the whole functional equations that can be applied to any setting (not necessarily analytic) in which Bernstein-Sato polynomials can be defined.","authors_text":"Alberto Casta\\~no Dom\\'inguez, Luis Narv\\'aez Macarro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-25T20:37:35Z","title":"On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.14368","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":"sha256:9be3efda0c12bf3cc966ad2222a28f27a2a4a8e61aaabbd83d52a6bf6fd56ec2","target":"record","created_at":"2026-07-05T06:48:46Z","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":"2be1a76784839791304eaabee6d1299e532e1e228cddc256e6df37ad3973d62c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-11-25T20:37:35Z","title_canon_sha256":"0ce2326dfaaa3b719ef7bacf8cb3e1fdec05c749dc2c837d834900755d3ea6b0"},"schema_version":"1.0","source":{"id":"2211.14368","kind":"arxiv","version":2}},"canonical_sha256":"2a45a143753e5cfdec7fdab1ae14e96d002cc76ecc6e6ec605cb1dfb5778f635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a45a143753e5cfdec7fdab1ae14e96d002cc76ecc6e6ec605cb1dfb5778f635","first_computed_at":"2026-07-05T06:48:46.290699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:48:46.290699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mWy1BjHOGxTHjrURFoG+h1UnAPYQtd9qzt7KC59bEg9etyGz6nUXZFnrSsckTnAul2Td6Cti/AB2Pudg8tgmBw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:48:46.291184Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.14368","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9be3efda0c12bf3cc966ad2222a28f27a2a4a8e61aaabbd83d52a6bf6fd56ec2","sha256:17fe6a73db055a65e5c180b8855b005b5346b02b207fb909c8a80c22fe2bc3fe"],"state_sha256":"03e79e2b15231accbae7d5abd9d5ec61c44cd76ddb27c2c18a9f488481ca3b16"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CVIdff1I6Uz5FDz2ATJ1UvsRNe1rRYT3RBgr+f0/1+VeuEUEyuX3F6+boMHIUI3pWE1yjE6rQIwqKSuhdXpEAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T16:25:10.667443Z","bundle_sha256":"50073e4677fa8055e73bba8f73234ae4917fa1a301b8793511ce353b82fff9e7"}}