{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:HDB3EXMCI3HYVOCCKAM5WDMJFE","short_pith_number":"pith:HDB3EXMC","canonical_record":{"source":{"id":"math/0401344","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2004-01-25T17:31:44Z","cross_cats_sorted":[],"title_canon_sha256":"e85876bd5cd45707eae02184909a35288a25b5aeca57a5493868090e29c63e25","abstract_canon_sha256":"43200513148e7a6cf98875379c100c6aa4d76c1f995cf252e9f73625e332c076"},"schema_version":"1.0"},"canonical_sha256":"38c3b25d8246cf8ab8425019db0d892914d085eb137fdb199f94174a80bfe183","source":{"kind":"arxiv","id":"math/0401344","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401344","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401344v2","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401344","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"HDB3EXMCI3HY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"HDB3EXMCI3HYVOCC","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"HDB3EXMC","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:HDB3EXMCI3HYVOCCKAM5WDMJFE","target":"record","payload":{"canonical_record":{"source":{"id":"math/0401344","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2004-01-25T17:31:44Z","cross_cats_sorted":[],"title_canon_sha256":"e85876bd5cd45707eae02184909a35288a25b5aeca57a5493868090e29c63e25","abstract_canon_sha256":"43200513148e7a6cf98875379c100c6aa4d76c1f995cf252e9f73625e332c076"},"schema_version":"1.0"},"canonical_sha256":"38c3b25d8246cf8ab8425019db0d892914d085eb137fdb199f94174a80bfe183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:31.695769Z","signature_b64":"lQccV3PGSnG3AsA0iE07EKVdY2xaQF33hlf3c8yfJw4h4lvgNgphhwFBrkSHF/3J7CKKg8919HS4R2Tw+3gkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38c3b25d8246cf8ab8425019db0d892914d085eb137fdb199f94174a80bfe183","last_reissued_at":"2026-05-17T23:41:31.695043Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:31.695043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0401344","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":"2026-05-17T23:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uKmgdUIXFe7693LTUApcxp/eBgjOo/i16UvCLDOV2E2h1mY0c+jqeczFFLlGfM6avU54UU0xUXC32oJdwCpEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:26:34.317940Z"},"content_sha256":"6b68cfab81e89444a70146a44de667dd687fdac5b00966bed270158794204f82","schema_version":"1.0","event_id":"sha256:6b68cfab81e89444a70146a44de667dd687fdac5b00966bed270158794204f82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:HDB3EXMCI3HYVOCCKAM5WDMJFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The deformation theory of representations of the fundamental group of a smooth variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J. P. Pridham","submitted_at":"2004-01-25T17:31:44Z","abstract_excerpt":"Consider the functor describing deformations of a representation of the fundamental group of a variety X. This paper is chiefly concerned with establishing an analogue in finite characteristic of a result proved by Goldman and Millson for compact Kahler manifolds. By applying the Weil Conjectures instead of Hodge theory, we see that if X is a smooth proper variety defined over a finite field, and we consider deformations of certain continuous l-adic representations of the algebraic fundamental group, then the hull of the deformation functor will be defined by quadratic equations. Moreover, if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401344","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":""},"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":"2026-05-17T23:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmNmFS1EcQkHhJxZ7lSx6djZWjf2IfEkymSmXnGXlxjHiEmrWPU75TMt5Zgz2SQULAanKLC9Uz2OTWI4S74eCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:26:34.318276Z"},"content_sha256":"59174ad1e5f336dbac8a71824d443f509cd60e281fda6e97f5a2980b827f9304","schema_version":"1.0","event_id":"sha256:59174ad1e5f336dbac8a71824d443f509cd60e281fda6e97f5a2980b827f9304"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HDB3EXMCI3HYVOCCKAM5WDMJFE/bundle.json","state_url":"https://pith.science/pith/HDB3EXMCI3HYVOCCKAM5WDMJFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HDB3EXMCI3HYVOCCKAM5WDMJFE/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":"2026-07-01T18:26:34Z","links":{"resolver":"https://pith.science/pith/HDB3EXMCI3HYVOCCKAM5WDMJFE","bundle":"https://pith.science/pith/HDB3EXMCI3HYVOCCKAM5WDMJFE/bundle.json","state":"https://pith.science/pith/HDB3EXMCI3HYVOCCKAM5WDMJFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HDB3EXMCI3HYVOCCKAM5WDMJFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:HDB3EXMCI3HYVOCCKAM5WDMJFE","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":"43200513148e7a6cf98875379c100c6aa4d76c1f995cf252e9f73625e332c076","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2004-01-25T17:31:44Z","title_canon_sha256":"e85876bd5cd45707eae02184909a35288a25b5aeca57a5493868090e29c63e25"},"schema_version":"1.0","source":{"id":"math/0401344","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401344","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401344v2","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401344","created_at":"2026-05-17T23:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"HDB3EXMCI3HY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"HDB3EXMCI3HYVOCC","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"HDB3EXMC","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:59174ad1e5f336dbac8a71824d443f509cd60e281fda6e97f5a2980b827f9304","target":"graph","created_at":"2026-05-17T23:41:31Z","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":"Consider the functor describing deformations of a representation of the fundamental group of a variety X. This paper is chiefly concerned with establishing an analogue in finite characteristic of a result proved by Goldman and Millson for compact Kahler manifolds. By applying the Weil Conjectures instead of Hodge theory, we see that if X is a smooth proper variety defined over a finite field, and we consider deformations of certain continuous l-adic representations of the algebraic fundamental group, then the hull of the deformation functor will be defined by quadratic equations. Moreover, if ","authors_text":"J. P. Pridham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2004-01-25T17:31:44Z","title":"The deformation theory of representations of the fundamental group of a smooth variety"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401344","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":"sha256:6b68cfab81e89444a70146a44de667dd687fdac5b00966bed270158794204f82","target":"record","created_at":"2026-05-17T23:41:31Z","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":"43200513148e7a6cf98875379c100c6aa4d76c1f995cf252e9f73625e332c076","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2004-01-25T17:31:44Z","title_canon_sha256":"e85876bd5cd45707eae02184909a35288a25b5aeca57a5493868090e29c63e25"},"schema_version":"1.0","source":{"id":"math/0401344","kind":"arxiv","version":2}},"canonical_sha256":"38c3b25d8246cf8ab8425019db0d892914d085eb137fdb199f94174a80bfe183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38c3b25d8246cf8ab8425019db0d892914d085eb137fdb199f94174a80bfe183","first_computed_at":"2026-05-17T23:41:31.695043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:31.695043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lQccV3PGSnG3AsA0iE07EKVdY2xaQF33hlf3c8yfJw4h4lvgNgphhwFBrkSHF/3J7CKKg8919HS4R2Tw+3gkBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:31.695769Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401344","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b68cfab81e89444a70146a44de667dd687fdac5b00966bed270158794204f82","sha256:59174ad1e5f336dbac8a71824d443f509cd60e281fda6e97f5a2980b827f9304"],"state_sha256":"d7cf49b2e5585446c8791d6c9c16c1f2003231261e5c0efe8169c545a2f280ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bh4kRIVqyrBoj4u9y2lFIKIVWRXDmIg+4Y86NizAZ4CggpwGz3SafJomv0PuPXjIhZ2DXVPq+o3gdC6XLpnAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T18:26:34.320089Z","bundle_sha256":"5f54925ae2f05295fee7ca83a621219e10be4be51a31d78dbd09f89c6c79f1b6"}}