{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:TZXHTAV3RHQYUEJHCGOX6EJCSA","short_pith_number":"pith:TZXHTAV3","canonical_record":{"source":{"id":"2102.03384","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-05T19:08:47Z","cross_cats_sorted":["math.AG","math.LO"],"title_canon_sha256":"786af639498b7081553bd35a1e2b43646ef5edaa1551d7b5a628b7cd8c5d995d","abstract_canon_sha256":"6f24351124ad12061b30f3a362459840e68b0140eb35c346c6d710f59bb736d3"},"schema_version":"1.0"},"canonical_sha256":"9e6e7982bb89e18a1127119d7f1122901092c474c5546b74a12e7b608b17e2f0","source":{"kind":"arxiv","id":"2102.03384","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.03384","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"2102.03384v5","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.03384","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"TZXHTAV3RHQY","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"pith_short_16","alias_value":"TZXHTAV3RHQYUEJH","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"pith_short_8","alias_value":"TZXHTAV3","created_at":"2026-06-02T03:04:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:TZXHTAV3RHQYUEJHCGOX6EJCSA","target":"record","payload":{"canonical_record":{"source":{"id":"2102.03384","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-05T19:08:47Z","cross_cats_sorted":["math.AG","math.LO"],"title_canon_sha256":"786af639498b7081553bd35a1e2b43646ef5edaa1551d7b5a628b7cd8c5d995d","abstract_canon_sha256":"6f24351124ad12061b30f3a362459840e68b0140eb35c346c6d710f59bb736d3"},"schema_version":"1.0"},"canonical_sha256":"9e6e7982bb89e18a1127119d7f1122901092c474c5546b74a12e7b608b17e2f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:04:29.682631Z","signature_b64":"BUG+gnf+PZ5OTeBHfv75vRTyiluKPrCB4uKvU4p+EsQeuauVrl39dxInKjjz8rp4rVB+VzjNuvuMOvuw4AaLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e6e7982bb89e18a1127119d7f1122901092c474c5546b74a12e7b608b17e2f0","last_reissued_at":"2026-06-02T03:04:29.682050Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:04:29.682050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.03384","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T03:04:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lMM4S0/XDYJ9w6sbAzCOGgV9mjVzDz2bje2fuVC1x/F32aOofMqopEfmcA5y6hxRiq/MRsRPjqq8nFLGX997Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:45:23.569101Z"},"content_sha256":"5e2425aa324ac13567829ee5bdd36681c63ee76302afffb7ccd924050dbe99c2","schema_version":"1.0","event_id":"sha256:5e2425aa324ac13567829ee5bdd36681c63ee76302afffb7ccd924050dbe99c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:TZXHTAV3RHQYUEJHCGOX6EJCSA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A differential approach to Ax-Schanuel, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO"],"primary_cat":"math.NT","authors_text":"David Bl\\'azquez-Sanz, Guy Casale, James Freitag, Joel Nagloo","submitted_at":"2021-02-05T19:08:47Z","abstract_excerpt":"In this paper, we prove several Ax-Schanuel type results for uniformizers of geometric structures; our general results describe the differential algebraic relations between the solutions of the partial differential equations satisfied by the uniformizers. In particular, we give a proof of the full Ax-Schanuel Theorem with derivatives for uniformizers of simple projective structure on curves including unifomizers of any Fuchsian group of the first kind and any genus.\n  Combining our techniques with those of Ax, we give a strong Ax-Schanuel result for the combination of the derivatives of the j-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.03384","kind":"arxiv","version":5},"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/2102.03384/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":"2026-06-02T03:04:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZSdqpcv3UYiYdvY5dnLK/JFIYyaAaRSOcVWMaK6PpGXWHe9n9kB/waVARKMDgXMY2IK45hQNNjnX9lZdu2n9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:45:23.569498Z"},"content_sha256":"32f08dafbf07f9240412175b7966f4a37b0f0edf348022b49aceb0269fae589b","schema_version":"1.0","event_id":"sha256:32f08dafbf07f9240412175b7966f4a37b0f0edf348022b49aceb0269fae589b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TZXHTAV3RHQYUEJHCGOX6EJCSA/bundle.json","state_url":"https://pith.science/pith/TZXHTAV3RHQYUEJHCGOX6EJCSA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TZXHTAV3RHQYUEJHCGOX6EJCSA/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":"2026-06-11T09:45:23Z","links":{"resolver":"https://pith.science/pith/TZXHTAV3RHQYUEJHCGOX6EJCSA","bundle":"https://pith.science/pith/TZXHTAV3RHQYUEJHCGOX6EJCSA/bundle.json","state":"https://pith.science/pith/TZXHTAV3RHQYUEJHCGOX6EJCSA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TZXHTAV3RHQYUEJHCGOX6EJCSA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TZXHTAV3RHQYUEJHCGOX6EJCSA","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":"6f24351124ad12061b30f3a362459840e68b0140eb35c346c6d710f59bb736d3","cross_cats_sorted":["math.AG","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-05T19:08:47Z","title_canon_sha256":"786af639498b7081553bd35a1e2b43646ef5edaa1551d7b5a628b7cd8c5d995d"},"schema_version":"1.0","source":{"id":"2102.03384","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.03384","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"2102.03384v5","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.03384","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"TZXHTAV3RHQY","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"pith_short_16","alias_value":"TZXHTAV3RHQYUEJH","created_at":"2026-06-02T03:04:29Z"},{"alias_kind":"pith_short_8","alias_value":"TZXHTAV3","created_at":"2026-06-02T03:04:29Z"}],"graph_snapshots":[{"event_id":"sha256:32f08dafbf07f9240412175b7966f4a37b0f0edf348022b49aceb0269fae589b","target":"graph","created_at":"2026-06-02T03:04:29Z","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/2102.03384/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove several Ax-Schanuel type results for uniformizers of geometric structures; our general results describe the differential algebraic relations between the solutions of the partial differential equations satisfied by the uniformizers. In particular, we give a proof of the full Ax-Schanuel Theorem with derivatives for uniformizers of simple projective structure on curves including unifomizers of any Fuchsian group of the first kind and any genus.\n  Combining our techniques with those of Ax, we give a strong Ax-Schanuel result for the combination of the derivatives of the j-","authors_text":"David Bl\\'azquez-Sanz, Guy Casale, James Freitag, Joel Nagloo","cross_cats":["math.AG","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-05T19:08:47Z","title":"A differential approach to Ax-Schanuel, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.03384","kind":"arxiv","version":5},"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":"sha256:5e2425aa324ac13567829ee5bdd36681c63ee76302afffb7ccd924050dbe99c2","target":"record","created_at":"2026-06-02T03:04:29Z","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":"6f24351124ad12061b30f3a362459840e68b0140eb35c346c6d710f59bb736d3","cross_cats_sorted":["math.AG","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-05T19:08:47Z","title_canon_sha256":"786af639498b7081553bd35a1e2b43646ef5edaa1551d7b5a628b7cd8c5d995d"},"schema_version":"1.0","source":{"id":"2102.03384","kind":"arxiv","version":5}},"canonical_sha256":"9e6e7982bb89e18a1127119d7f1122901092c474c5546b74a12e7b608b17e2f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e6e7982bb89e18a1127119d7f1122901092c474c5546b74a12e7b608b17e2f0","first_computed_at":"2026-06-02T03:04:29.682050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:04:29.682050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BUG+gnf+PZ5OTeBHfv75vRTyiluKPrCB4uKvU4p+EsQeuauVrl39dxInKjjz8rp4rVB+VzjNuvuMOvuw4AaLDg==","signature_status":"signed_v1","signed_at":"2026-06-02T03:04:29.682631Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.03384","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e2425aa324ac13567829ee5bdd36681c63ee76302afffb7ccd924050dbe99c2","sha256:32f08dafbf07f9240412175b7966f4a37b0f0edf348022b49aceb0269fae589b"],"state_sha256":"740e2d7be820d62e934b33edbda525a509035c3da6d042940d039bce30db8cf4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vpa74WMeR2eLxmosahwaKitkLZANPhHD4sCaQJLtbAkkE00bIVQpbG3UEvKLwWU6Iu6tN+zHK0kPHZNrmBkMDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:45:23.571379Z","bundle_sha256":"bb7bc1a2ae590ec0f249de54c7a08453a40782fc5df361244d0715ba4254d488"}}