{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QTI467MXU7NTZBEHLIV2XUIOTJ","short_pith_number":"pith:QTI467MX","canonical_record":{"source":{"id":"1103.0468","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-02T16:12:02Z","cross_cats_sorted":["math.AG","math.MP"],"title_canon_sha256":"42c44465a1951a24ff444e9622fc2f4444071b1e3745fa1c36032be680586656","abstract_canon_sha256":"fd3fce3f453c66fbc68efacde0ef03429cda89f99b9d8be05f4e019ea8816537"},"schema_version":"1.0"},"canonical_sha256":"84d1cf7d97a7db3c84875a2babd10e9a6356301050b6792d899d8da3cbddf974","source":{"kind":"arxiv","id":"1103.0468","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0468","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0468v2","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0468","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"pith_short_12","alias_value":"QTI467MXU7NT","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QTI467MXU7NTZBEH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QTI467MX","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QTI467MXU7NTZBEHLIV2XUIOTJ","target":"record","payload":{"canonical_record":{"source":{"id":"1103.0468","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-02T16:12:02Z","cross_cats_sorted":["math.AG","math.MP"],"title_canon_sha256":"42c44465a1951a24ff444e9622fc2f4444071b1e3745fa1c36032be680586656","abstract_canon_sha256":"fd3fce3f453c66fbc68efacde0ef03429cda89f99b9d8be05f4e019ea8816537"},"schema_version":"1.0"},"canonical_sha256":"84d1cf7d97a7db3c84875a2babd10e9a6356301050b6792d899d8da3cbddf974","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:27.409819Z","signature_b64":"kRMaAjIqpaYOccOv8lh/hMYbUrZp/CMizNBdb0mVlIJYGmZQQlt5i59UGU3g3Jd2FciDv+tv2MNCoBTLIAflBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84d1cf7d97a7db3c84875a2babd10e9a6356301050b6792d899d8da3cbddf974","last_reissued_at":"2026-05-18T02:53:27.409067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:27.409067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.0468","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":"2026-05-18T02:53:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FKuNiHGa9/JL0FUy/KIdDZ2B7JQbHXjg8QXZtkVUsz519u4mZKMVsE0K/sqktb1CgJ2itpWbXIPbEGbfF+79Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:11:03.583819Z"},"content_sha256":"11186203fc707d8bcd5eb00c6ced516dd188d53ccf907f3547a2485ba4800e6e","schema_version":"1.0","event_id":"sha256:11186203fc707d8bcd5eb00c6ced516dd188d53ccf907f3547a2485ba4800e6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QTI467MXU7NTZBEHLIV2XUIOTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deriving bases for Abelian functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP"],"primary_cat":"math-ph","authors_text":"Matthew England","submitted_at":"2011-03-02T16:12:02Z","abstract_excerpt":"We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated with a trigonal curve of genus four. The main motivation for the construction of such bases is that it allows systematic methods for the derivation of the addition formulae and differential equations satisfied by the functions. We present a new 3-term 2-variable addition formulae and a complete set of differential equations to generalise the classic Weierstra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0468","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":"2026-05-18T02:53:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vN+gxrNsfzYpV7xOnYW2xDkG3IV/M43h+VkUIKMcBoGh/262ElBGAdoKzEpbjowE1AkVubDhdo9NYEIof6bLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:11:03.584157Z"},"content_sha256":"bdb417438cb9e9d158ec420dad5facf0b998489e66e4b7a856f8f52310f7ab2d","schema_version":"1.0","event_id":"sha256:bdb417438cb9e9d158ec420dad5facf0b998489e66e4b7a856f8f52310f7ab2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QTI467MXU7NTZBEHLIV2XUIOTJ/bundle.json","state_url":"https://pith.science/pith/QTI467MXU7NTZBEHLIV2XUIOTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QTI467MXU7NTZBEHLIV2XUIOTJ/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":"2026-06-02T13:11:03Z","links":{"resolver":"https://pith.science/pith/QTI467MXU7NTZBEHLIV2XUIOTJ","bundle":"https://pith.science/pith/QTI467MXU7NTZBEHLIV2XUIOTJ/bundle.json","state":"https://pith.science/pith/QTI467MXU7NTZBEHLIV2XUIOTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QTI467MXU7NTZBEHLIV2XUIOTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QTI467MXU7NTZBEHLIV2XUIOTJ","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":"fd3fce3f453c66fbc68efacde0ef03429cda89f99b9d8be05f4e019ea8816537","cross_cats_sorted":["math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-02T16:12:02Z","title_canon_sha256":"42c44465a1951a24ff444e9622fc2f4444071b1e3745fa1c36032be680586656"},"schema_version":"1.0","source":{"id":"1103.0468","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0468","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0468v2","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0468","created_at":"2026-05-18T02:53:27Z"},{"alias_kind":"pith_short_12","alias_value":"QTI467MXU7NT","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QTI467MXU7NTZBEH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QTI467MX","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:bdb417438cb9e9d158ec420dad5facf0b998489e66e4b7a856f8f52310f7ab2d","target":"graph","created_at":"2026-05-18T02:53:27Z","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 present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated with a trigonal curve of genus four. The main motivation for the construction of such bases is that it allows systematic methods for the derivation of the addition formulae and differential equations satisfied by the functions. We present a new 3-term 2-variable addition formulae and a complete set of differential equations to generalise the classic Weierstra","authors_text":"Matthew England","cross_cats":["math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-02T16:12:02Z","title":"Deriving bases for Abelian functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0468","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":"sha256:11186203fc707d8bcd5eb00c6ced516dd188d53ccf907f3547a2485ba4800e6e","target":"record","created_at":"2026-05-18T02:53:27Z","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":"fd3fce3f453c66fbc68efacde0ef03429cda89f99b9d8be05f4e019ea8816537","cross_cats_sorted":["math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-02T16:12:02Z","title_canon_sha256":"42c44465a1951a24ff444e9622fc2f4444071b1e3745fa1c36032be680586656"},"schema_version":"1.0","source":{"id":"1103.0468","kind":"arxiv","version":2}},"canonical_sha256":"84d1cf7d97a7db3c84875a2babd10e9a6356301050b6792d899d8da3cbddf974","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84d1cf7d97a7db3c84875a2babd10e9a6356301050b6792d899d8da3cbddf974","first_computed_at":"2026-05-18T02:53:27.409067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:27.409067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kRMaAjIqpaYOccOv8lh/hMYbUrZp/CMizNBdb0mVlIJYGmZQQlt5i59UGU3g3Jd2FciDv+tv2MNCoBTLIAflBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:27.409819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0468","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11186203fc707d8bcd5eb00c6ced516dd188d53ccf907f3547a2485ba4800e6e","sha256:bdb417438cb9e9d158ec420dad5facf0b998489e66e4b7a856f8f52310f7ab2d"],"state_sha256":"c2d2d7b50f96c30b0c35dba2b05620f72241de8b47c0d23bf338aeabc6827bbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fo+e1p0mGuIi75PTxpLsi6vG+usMiyQGJrs4+DK4EyrSkYHjpATP6lvByGQLirVwbSzFhHaoFzMHDH5/55HMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:11:03.586076Z","bundle_sha256":"47bb750b043c4f46ce2aadf6e1b669b7c97331bf8fa2f2e65b129c99a2e0cf60"}}