{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VQISGFOJ2VHTNN2RERCWOLAP67","short_pith_number":"pith:VQISGFOJ","canonical_record":{"source":{"id":"2501.04716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T02:44:01Z","cross_cats_sorted":[],"title_canon_sha256":"8aaf510ed3f672f2d117bdb565086f9ae518c43fefdafc898fb381c62f06302a","abstract_canon_sha256":"5701343545a3cfba2b5d2b6e54662ce3ff23c55fbe681f937c4997d613392002"},"schema_version":"1.0"},"canonical_sha256":"ac112315c9d54f36b7512445672c0ff7e736bb0fece34995505af669e141cd94","source":{"kind":"arxiv","id":"2501.04716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04716","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04716v1","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04716","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"pith_short_12","alias_value":"VQISGFOJ2VHT","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"pith_short_16","alias_value":"VQISGFOJ2VHTNN2R","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"pith_short_8","alias_value":"VQISGFOJ","created_at":"2026-07-05T09:58:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VQISGFOJ2VHTNN2RERCWOLAP67","target":"record","payload":{"canonical_record":{"source":{"id":"2501.04716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T02:44:01Z","cross_cats_sorted":[],"title_canon_sha256":"8aaf510ed3f672f2d117bdb565086f9ae518c43fefdafc898fb381c62f06302a","abstract_canon_sha256":"5701343545a3cfba2b5d2b6e54662ce3ff23c55fbe681f937c4997d613392002"},"schema_version":"1.0"},"canonical_sha256":"ac112315c9d54f36b7512445672c0ff7e736bb0fece34995505af669e141cd94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:58:45.350275Z","signature_b64":"Clsz3Ya8QxBw9h+0V2TrIeBXCeCxuw5kthyrvuUvKKO8fBN67rEnFaCMD6Cd7URpoTNAMLcENJPAzbxImN1DAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac112315c9d54f36b7512445672c0ff7e736bb0fece34995505af669e141cd94","last_reissued_at":"2026-07-05T09:58:45.349831Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:58:45.349831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.04716","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":"2026-07-05T09:58:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tOV0yVSHiBbGYGWBlX4ruxjNdRSaf3SoFXd3TMCewtIuQpAGGr9YU6/AC12rTYQ1FirXvMEqiFwmVYjRoqlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:56:51.643566Z"},"content_sha256":"b9259c62ad14d46b8438472f51a6b448eac539392cc58823d77e783618f666bf","schema_version":"1.0","event_id":"sha256:b9259c62ad14d46b8438472f51a6b448eac539392cc58823d77e783618f666bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VQISGFOJ2VHTNN2RERCWOLAP67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some recent results on the punctual Quot schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chandranandan Gangopadhyay, Indranil Biswas, Ronnie Sebastian","submitted_at":"2025-01-02T02:44:01Z","abstract_excerpt":"Let $C$ be a smooth projective curve defined over the field of complex numbers. Let $E$ be a vector bundle on $C$, and fix an integer $d\\geqslant 1$. Let $\\mc Q:={\\rm Quot}(E,d)$ be the Quot Scheme which parameterizes all torsion quotients of $E$ of degree $d$. In this article, we survey some recent results on various invariants of $\\mc Q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04716","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.04716/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":"2026-07-05T09:58:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/49+Oj7qsS13FWzy1BIGBM3IH67zX+Nv5LdfVQ+GY0b6Yv8LQHQA9a0BWE9jAjRWqzOgGBERw8f+mbP5q1dCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T03:56:51.643935Z"},"content_sha256":"092ff1d5debf85cadb4207066443a0d728224a8862df7815ebc0bc45fc35d8fd","schema_version":"1.0","event_id":"sha256:092ff1d5debf85cadb4207066443a0d728224a8862df7815ebc0bc45fc35d8fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQISGFOJ2VHTNN2RERCWOLAP67/bundle.json","state_url":"https://pith.science/pith/VQISGFOJ2VHTNN2RERCWOLAP67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQISGFOJ2VHTNN2RERCWOLAP67/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":"2026-07-09T03:56:51Z","links":{"resolver":"https://pith.science/pith/VQISGFOJ2VHTNN2RERCWOLAP67","bundle":"https://pith.science/pith/VQISGFOJ2VHTNN2RERCWOLAP67/bundle.json","state":"https://pith.science/pith/VQISGFOJ2VHTNN2RERCWOLAP67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQISGFOJ2VHTNN2RERCWOLAP67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VQISGFOJ2VHTNN2RERCWOLAP67","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":"5701343545a3cfba2b5d2b6e54662ce3ff23c55fbe681f937c4997d613392002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T02:44:01Z","title_canon_sha256":"8aaf510ed3f672f2d117bdb565086f9ae518c43fefdafc898fb381c62f06302a"},"schema_version":"1.0","source":{"id":"2501.04716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04716","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04716v1","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04716","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"pith_short_12","alias_value":"VQISGFOJ2VHT","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"pith_short_16","alias_value":"VQISGFOJ2VHTNN2R","created_at":"2026-07-05T09:58:45Z"},{"alias_kind":"pith_short_8","alias_value":"VQISGFOJ","created_at":"2026-07-05T09:58:45Z"}],"graph_snapshots":[{"event_id":"sha256:092ff1d5debf85cadb4207066443a0d728224a8862df7815ebc0bc45fc35d8fd","target":"graph","created_at":"2026-07-05T09:58:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.04716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $C$ be a smooth projective curve defined over the field of complex numbers. Let $E$ be a vector bundle on $C$, and fix an integer $d\\geqslant 1$. Let $\\mc Q:={\\rm Quot}(E,d)$ be the Quot Scheme which parameterizes all torsion quotients of $E$ of degree $d$. In this article, we survey some recent results on various invariants of $\\mc Q$.","authors_text":"Chandranandan Gangopadhyay, Indranil Biswas, Ronnie Sebastian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T02:44:01Z","title":"Some recent results on the punctual Quot schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04716","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:b9259c62ad14d46b8438472f51a6b448eac539392cc58823d77e783618f666bf","target":"record","created_at":"2026-07-05T09:58:45Z","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":"5701343545a3cfba2b5d2b6e54662ce3ff23c55fbe681f937c4997d613392002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T02:44:01Z","title_canon_sha256":"8aaf510ed3f672f2d117bdb565086f9ae518c43fefdafc898fb381c62f06302a"},"schema_version":"1.0","source":{"id":"2501.04716","kind":"arxiv","version":1}},"canonical_sha256":"ac112315c9d54f36b7512445672c0ff7e736bb0fece34995505af669e141cd94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac112315c9d54f36b7512445672c0ff7e736bb0fece34995505af669e141cd94","first_computed_at":"2026-07-05T09:58:45.349831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:58:45.349831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Clsz3Ya8QxBw9h+0V2TrIeBXCeCxuw5kthyrvuUvKKO8fBN67rEnFaCMD6Cd7URpoTNAMLcENJPAzbxImN1DAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:58:45.350275Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.04716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9259c62ad14d46b8438472f51a6b448eac539392cc58823d77e783618f666bf","sha256:092ff1d5debf85cadb4207066443a0d728224a8862df7815ebc0bc45fc35d8fd"],"state_sha256":"556157f1849033b24b79a305d7452bc10e711cf4d29d66399a1e60f745868da8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j0tP6BJFWG87JJiL0l96DswXR8Z2IG+Ew27LOUDid6qntA/tkkpEcVKSt7oVT1CKHJY8ympQx3w1sA3Byr5pCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T03:56:51.645988Z","bundle_sha256":"6de41abdc373ac772f5288cb9af3590a4a23ae40552d81756a27b347976d0871"}}