{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MMGN4DTB2O6BLE3QOPTB24O5PH","short_pith_number":"pith:MMGN4DTB","canonical_record":{"source":{"id":"1601.05127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-19T22:53:24Z","cross_cats_sorted":[],"title_canon_sha256":"92121b55a7c1c0d527f38cd6745fb3d46acc9833ad82dee75eb490e13383182d","abstract_canon_sha256":"a89e318139baca44fb0dd91080512bcfd4ec577a1fe2b04d5dec925df4c47c4a"},"schema_version":"1.0"},"canonical_sha256":"630cde0e61d3bc15937073e61d71dd79d13b1f25e9c6622072ba45906e5f4cc5","source":{"kind":"arxiv","id":"1601.05127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05127","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05127v1","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05127","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"MMGN4DTB2O6B","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MMGN4DTB2O6BLE3Q","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MMGN4DTB","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MMGN4DTB2O6BLE3QOPTB24O5PH","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-19T22:53:24Z","cross_cats_sorted":[],"title_canon_sha256":"92121b55a7c1c0d527f38cd6745fb3d46acc9833ad82dee75eb490e13383182d","abstract_canon_sha256":"a89e318139baca44fb0dd91080512bcfd4ec577a1fe2b04d5dec925df4c47c4a"},"schema_version":"1.0"},"canonical_sha256":"630cde0e61d3bc15937073e61d71dd79d13b1f25e9c6622072ba45906e5f4cc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:16.060342Z","signature_b64":"RLHq+MM5bPv9qYABbtXsNt5mSwOCwX6UeinvtDDn/NJMYxvfOYxziQAQ7BqTPFugn1MXSwGPUNawOg/dYYcdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"630cde0e61d3bc15937073e61d71dd79d13b1f25e9c6622072ba45906e5f4cc5","last_reissued_at":"2026-05-18T01:22:16.059636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:16.059636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05127","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Lw4IxF/VAptHBY9Th1+XaDkyOz8sIib7asNnqv832n3DJrDf/kPUIGbusGUK2L52Bg7AFkv+4kWqjEai0bsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:16:20.889734Z"},"content_sha256":"310bc49150ae1b71de1c125a35433f6de58219a34dbc4d29160081e7f9e06a2d","schema_version":"1.0","event_id":"sha256:310bc49150ae1b71de1c125a35433f6de58219a34dbc4d29160081e7f9e06a2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MMGN4DTB2O6BLE3QOPTB24O5PH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A-hypergeometric series and the Hasse-Witt matrix of a hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alan Adolphson, Steven Sperber","submitted_at":"2016-01-19T22:53:24Z","abstract_excerpt":"We give a short combinatorial proof of the generic invertibility of the Hasse-Witt matrix of a projective hypersurface. We also examine the relationship between the Hasse-Witt matrix and certain $A$-hypergeometric series, which is what motivated the proof."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05127","kind":"arxiv","version":1},"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":"2026-05-18T01:22:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4qi051i7kh1S9roegs0KNB1HgoZtUX8clCU13a1ztfU46cjoaAl9i0k+cJSy9+4IDKPEdowqez3DcctEHf4WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:16:20.890211Z"},"content_sha256":"fde046262500aa6d0e502ef5cbbeb18ba6394beb2ed792208e5b4633cf61e738","schema_version":"1.0","event_id":"sha256:fde046262500aa6d0e502ef5cbbeb18ba6394beb2ed792208e5b4633cf61e738"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MMGN4DTB2O6BLE3QOPTB24O5PH/bundle.json","state_url":"https://pith.science/pith/MMGN4DTB2O6BLE3QOPTB24O5PH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MMGN4DTB2O6BLE3QOPTB24O5PH/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":"2026-05-26T18:16:20Z","links":{"resolver":"https://pith.science/pith/MMGN4DTB2O6BLE3QOPTB24O5PH","bundle":"https://pith.science/pith/MMGN4DTB2O6BLE3QOPTB24O5PH/bundle.json","state":"https://pith.science/pith/MMGN4DTB2O6BLE3QOPTB24O5PH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MMGN4DTB2O6BLE3QOPTB24O5PH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MMGN4DTB2O6BLE3QOPTB24O5PH","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":"a89e318139baca44fb0dd91080512bcfd4ec577a1fe2b04d5dec925df4c47c4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-19T22:53:24Z","title_canon_sha256":"92121b55a7c1c0d527f38cd6745fb3d46acc9833ad82dee75eb490e13383182d"},"schema_version":"1.0","source":{"id":"1601.05127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05127","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05127v1","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05127","created_at":"2026-05-18T01:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"MMGN4DTB2O6B","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MMGN4DTB2O6BLE3Q","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MMGN4DTB","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:fde046262500aa6d0e502ef5cbbeb18ba6394beb2ed792208e5b4633cf61e738","target":"graph","created_at":"2026-05-18T01:22:16Z","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 give a short combinatorial proof of the generic invertibility of the Hasse-Witt matrix of a projective hypersurface. We also examine the relationship between the Hasse-Witt matrix and certain $A$-hypergeometric series, which is what motivated the proof.","authors_text":"Alan Adolphson, Steven Sperber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-19T22:53:24Z","title":"A-hypergeometric series and the Hasse-Witt matrix of a hypersurface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05127","kind":"arxiv","version":1},"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":"sha256:310bc49150ae1b71de1c125a35433f6de58219a34dbc4d29160081e7f9e06a2d","target":"record","created_at":"2026-05-18T01:22:16Z","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":"a89e318139baca44fb0dd91080512bcfd4ec577a1fe2b04d5dec925df4c47c4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-19T22:53:24Z","title_canon_sha256":"92121b55a7c1c0d527f38cd6745fb3d46acc9833ad82dee75eb490e13383182d"},"schema_version":"1.0","source":{"id":"1601.05127","kind":"arxiv","version":1}},"canonical_sha256":"630cde0e61d3bc15937073e61d71dd79d13b1f25e9c6622072ba45906e5f4cc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"630cde0e61d3bc15937073e61d71dd79d13b1f25e9c6622072ba45906e5f4cc5","first_computed_at":"2026-05-18T01:22:16.059636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:16.059636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RLHq+MM5bPv9qYABbtXsNt5mSwOCwX6UeinvtDDn/NJMYxvfOYxziQAQ7BqTPFugn1MXSwGPUNawOg/dYYcdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:16.060342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:310bc49150ae1b71de1c125a35433f6de58219a34dbc4d29160081e7f9e06a2d","sha256:fde046262500aa6d0e502ef5cbbeb18ba6394beb2ed792208e5b4633cf61e738"],"state_sha256":"7a460467cf48e34da2419f597e8734a6befaac6361be9fbd39a2d4230947c474"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/EEfmH16wlcShxQOYpEU+43C2+0y6Pb9QmFUCcHiqIuyAvX6gRQhl5iD3EgAPAs1NB2HUaczF/G2gY2yS+GlCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:16:20.893292Z","bundle_sha256":"95206295e5f73ebe9281ba6cf45dfa1b8c0122c383b8649adc17e565a3022c16"}}