{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5X2H772L6VRRIFLXLSGHBAXN3P","short_pith_number":"pith:5X2H772L","canonical_record":{"source":{"id":"1207.6130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-25T21:00:37Z","cross_cats_sorted":[],"title_canon_sha256":"95d8c118751fc9e735bddbabf0a2dabfa1c912e4725eb7d0d183e2cd0e8023ae","abstract_canon_sha256":"11b7a027fd44d0e5116846575933e96cd64870b4d97a1d4085a08406130ca781"},"schema_version":"1.0"},"canonical_sha256":"edf47fff4bf5631415775c8c7082eddbeff72c31d5c290fdd253fd4ee1626342","source":{"kind":"arxiv","id":"1207.6130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6130","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6130v1","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6130","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"pith_short_12","alias_value":"5X2H772L6VRR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5X2H772L6VRRIFLX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5X2H772L","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5X2H772L6VRRIFLXLSGHBAXN3P","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-25T21:00:37Z","cross_cats_sorted":[],"title_canon_sha256":"95d8c118751fc9e735bddbabf0a2dabfa1c912e4725eb7d0d183e2cd0e8023ae","abstract_canon_sha256":"11b7a027fd44d0e5116846575933e96cd64870b4d97a1d4085a08406130ca781"},"schema_version":"1.0"},"canonical_sha256":"edf47fff4bf5631415775c8c7082eddbeff72c31d5c290fdd253fd4ee1626342","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:08.768868Z","signature_b64":"j608YDPaeUP8ga42CfWN/Qnc9/7BFHphfzXMtUXFl6CEAmK39qnGcAZQCp6OB0/Pvb6nvBHk63GKwwv52gMJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edf47fff4bf5631415775c8c7082eddbeff72c31d5c290fdd253fd4ee1626342","last_reissued_at":"2026-05-18T03:50:08.767994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:08.767994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6130","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":"2026-05-18T03:50:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QgHKKyp0YcsfEY/EJPRMbXg5eeJTJKY6ITrZ3QywVww1VpfKB0t06RRYmW0C9Q7q80wN+fNHsdUlhU0MX3TZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:52:11.958560Z"},"content_sha256":"6842120de6249d3b052c16c2acc38634a645bd230c5ef6cf2bd432c9e7f3bffa","schema_version":"1.0","event_id":"sha256:6842120de6249d3b052c16c2acc38634a645bd230c5ef6cf2bd432c9e7f3bffa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5X2H772L6VRRIFLXLSGHBAXN3P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit bounds on canonical Green functions of modular curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Peter Bruin","submitted_at":"2012-07-25T21:00:37Z","abstract_excerpt":"We prove explicit bounds on canonical Green functions of Riemann surfaces obtained as compactifications of quotients of the upper half-plane by Fuchsian groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6130","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":"2026-05-18T03:50:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dxi9thqzSYYffc2lyT1r0iH/3Y7MQWmE3TZ+JZF1eHN15d5BCURYCo8lcxoHUdl3mqoqFcmumC7qfNQbwqVbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:52:11.958907Z"},"content_sha256":"6208eaed801574055a4d97241b70f1eff87d65469e3366dcafab886c552c573b","schema_version":"1.0","event_id":"sha256:6208eaed801574055a4d97241b70f1eff87d65469e3366dcafab886c552c573b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5X2H772L6VRRIFLXLSGHBAXN3P/bundle.json","state_url":"https://pith.science/pith/5X2H772L6VRRIFLXLSGHBAXN3P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5X2H772L6VRRIFLXLSGHBAXN3P/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":"2026-05-27T21:52:11Z","links":{"resolver":"https://pith.science/pith/5X2H772L6VRRIFLXLSGHBAXN3P","bundle":"https://pith.science/pith/5X2H772L6VRRIFLXLSGHBAXN3P/bundle.json","state":"https://pith.science/pith/5X2H772L6VRRIFLXLSGHBAXN3P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5X2H772L6VRRIFLXLSGHBAXN3P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5X2H772L6VRRIFLXLSGHBAXN3P","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":"11b7a027fd44d0e5116846575933e96cd64870b4d97a1d4085a08406130ca781","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-25T21:00:37Z","title_canon_sha256":"95d8c118751fc9e735bddbabf0a2dabfa1c912e4725eb7d0d183e2cd0e8023ae"},"schema_version":"1.0","source":{"id":"1207.6130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6130","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6130v1","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6130","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"pith_short_12","alias_value":"5X2H772L6VRR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5X2H772L6VRRIFLX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5X2H772L","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:6208eaed801574055a4d97241b70f1eff87d65469e3366dcafab886c552c573b","target":"graph","created_at":"2026-05-18T03:50:08Z","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 prove explicit bounds on canonical Green functions of Riemann surfaces obtained as compactifications of quotients of the upper half-plane by Fuchsian groups.","authors_text":"Peter Bruin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-25T21:00:37Z","title":"Explicit bounds on canonical Green functions of modular curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6130","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":"sha256:6842120de6249d3b052c16c2acc38634a645bd230c5ef6cf2bd432c9e7f3bffa","target":"record","created_at":"2026-05-18T03:50:08Z","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":"11b7a027fd44d0e5116846575933e96cd64870b4d97a1d4085a08406130ca781","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-25T21:00:37Z","title_canon_sha256":"95d8c118751fc9e735bddbabf0a2dabfa1c912e4725eb7d0d183e2cd0e8023ae"},"schema_version":"1.0","source":{"id":"1207.6130","kind":"arxiv","version":1}},"canonical_sha256":"edf47fff4bf5631415775c8c7082eddbeff72c31d5c290fdd253fd4ee1626342","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edf47fff4bf5631415775c8c7082eddbeff72c31d5c290fdd253fd4ee1626342","first_computed_at":"2026-05-18T03:50:08.767994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:08.767994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j608YDPaeUP8ga42CfWN/Qnc9/7BFHphfzXMtUXFl6CEAmK39qnGcAZQCp6OB0/Pvb6nvBHk63GKwwv52gMJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:08.768868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6842120de6249d3b052c16c2acc38634a645bd230c5ef6cf2bd432c9e7f3bffa","sha256:6208eaed801574055a4d97241b70f1eff87d65469e3366dcafab886c552c573b"],"state_sha256":"1715d69c0808848d0b92e8ef7acd510791ea49fc45a4168bf6c39cb2a6b15547"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BST2xpCGJdmaP6EEdBwOCXERtSCqR++Qm0DOjUk8Wv3l3xsJzOMfqTtYL7RMA7hTt2E4Uxui7ysY6jC/2zlzAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:52:11.961275Z","bundle_sha256":"ea1839bd7992591b43a2f731cd3c2178a3c6cbedbf9d4e59966f9edc9c600abe"}}