{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LQHP2OO4KE754PGQ5UUCNJ5BL2","short_pith_number":"pith:LQHP2OO4","canonical_record":{"source":{"id":"1403.6404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T16:14:41Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"2d449952d6f2b0b338dd4ae3301d373c0170f8bcd3c519fc374b6203ad295c21","abstract_canon_sha256":"c92048058e25628c2d37984840233b76aa3c5e24d2f95ef176cac7c7006f85cf"},"schema_version":"1.0"},"canonical_sha256":"5c0efd39dc513fde3cd0ed2826a7a15e97d0b8247202b8ffd9edaaef363f8f99","source":{"kind":"arxiv","id":"1403.6404","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6404","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6404v1","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6404","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"LQHP2OO4KE75","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LQHP2OO4KE754PGQ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LQHP2OO4","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LQHP2OO4KE754PGQ5UUCNJ5BL2","target":"record","payload":{"canonical_record":{"source":{"id":"1403.6404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T16:14:41Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"2d449952d6f2b0b338dd4ae3301d373c0170f8bcd3c519fc374b6203ad295c21","abstract_canon_sha256":"c92048058e25628c2d37984840233b76aa3c5e24d2f95ef176cac7c7006f85cf"},"schema_version":"1.0"},"canonical_sha256":"5c0efd39dc513fde3cd0ed2826a7a15e97d0b8247202b8ffd9edaaef363f8f99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:41.428220Z","signature_b64":"cuBfwF5u6dNXujQeQWpivwkDz8IQC41bUbtpjVuwVI0dDK4Ll270KGpw78U5CFPJZQA4kcrSCUhIjufxxMy/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c0efd39dc513fde3cd0ed2826a7a15e97d0b8247202b8ffd9edaaef363f8f99","last_reissued_at":"2026-05-18T02:51:41.427730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:41.427730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.6404","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":"2026-05-18T02:51:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9SbIvZafgXcz6p2cTP5vbFWDcdSuu93Wq8C0p6p9Kdqfe5IasGd8WtaAVSA8FcR/cPed/oqHjqb6BCNE89YDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:48:10.844547Z"},"content_sha256":"38aae9a80385d7fcbcd9c07b535a15adfc0874ecb2467bb7878fb20d5d40477b","schema_version":"1.0","event_id":"sha256:38aae9a80385d7fcbcd9c07b535a15adfc0874ecb2467bb7878fb20d5d40477b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LQHP2OO4KE754PGQ5UUCNJ5BL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial bounds for Arakelov invariants of Belyi curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Ariyan Javanpeykar, Peter Bruin","submitted_at":"2014-03-25T16:14:41Z","abstract_excerpt":"We explicitly bound the Faltings height of a curve over Q polynomially in its Belyi degree. Similar bounds are proven for three other Arakelov invariants: the discriminant, Faltings' delta invariant and the self-intersection of the dualizing sheaf. Our results allow us to explicitly bound Arakelov invariants of modular curves, Hurwitz curves and Fermat curves in terms of their genus. Moreover, as an application, we show that the Couveignes-Edixhoven-Bruin algorithm to compute coefficients of modular forms for congruence subgroups of SL2(Z) runs in polynomial time under the Riemann hypothesis f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6404","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":"2026-05-18T02:51:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vMr40wYZtP6/nQ7QWiHKBOW81q6avaj0+2WC4eNFGe4if2uVi86HSTXMlGIEOHswygsmwIPFWH07LsLciozACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:48:10.845202Z"},"content_sha256":"61fceab1b8ad02ee04293bcbb66d4441a3c0f15420293618899cfabc5238d3c9","schema_version":"1.0","event_id":"sha256:61fceab1b8ad02ee04293bcbb66d4441a3c0f15420293618899cfabc5238d3c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQHP2OO4KE754PGQ5UUCNJ5BL2/bundle.json","state_url":"https://pith.science/pith/LQHP2OO4KE754PGQ5UUCNJ5BL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQHP2OO4KE754PGQ5UUCNJ5BL2/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":"2026-05-27T23:48:10Z","links":{"resolver":"https://pith.science/pith/LQHP2OO4KE754PGQ5UUCNJ5BL2","bundle":"https://pith.science/pith/LQHP2OO4KE754PGQ5UUCNJ5BL2/bundle.json","state":"https://pith.science/pith/LQHP2OO4KE754PGQ5UUCNJ5BL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQHP2OO4KE754PGQ5UUCNJ5BL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LQHP2OO4KE754PGQ5UUCNJ5BL2","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":"c92048058e25628c2d37984840233b76aa3c5e24d2f95ef176cac7c7006f85cf","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T16:14:41Z","title_canon_sha256":"2d449952d6f2b0b338dd4ae3301d373c0170f8bcd3c519fc374b6203ad295c21"},"schema_version":"1.0","source":{"id":"1403.6404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6404","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6404v1","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6404","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"LQHP2OO4KE75","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LQHP2OO4KE754PGQ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LQHP2OO4","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:61fceab1b8ad02ee04293bcbb66d4441a3c0f15420293618899cfabc5238d3c9","target":"graph","created_at":"2026-05-18T02:51:41Z","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 explicitly bound the Faltings height of a curve over Q polynomially in its Belyi degree. Similar bounds are proven for three other Arakelov invariants: the discriminant, Faltings' delta invariant and the self-intersection of the dualizing sheaf. Our results allow us to explicitly bound Arakelov invariants of modular curves, Hurwitz curves and Fermat curves in terms of their genus. Moreover, as an application, we show that the Couveignes-Edixhoven-Bruin algorithm to compute coefficients of modular forms for congruence subgroups of SL2(Z) runs in polynomial time under the Riemann hypothesis f","authors_text":"Ariyan Javanpeykar, Peter Bruin","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T16:14:41Z","title":"Polynomial bounds for Arakelov invariants of Belyi curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6404","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":"sha256:38aae9a80385d7fcbcd9c07b535a15adfc0874ecb2467bb7878fb20d5d40477b","target":"record","created_at":"2026-05-18T02:51:41Z","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":"c92048058e25628c2d37984840233b76aa3c5e24d2f95ef176cac7c7006f85cf","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-25T16:14:41Z","title_canon_sha256":"2d449952d6f2b0b338dd4ae3301d373c0170f8bcd3c519fc374b6203ad295c21"},"schema_version":"1.0","source":{"id":"1403.6404","kind":"arxiv","version":1}},"canonical_sha256":"5c0efd39dc513fde3cd0ed2826a7a15e97d0b8247202b8ffd9edaaef363f8f99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c0efd39dc513fde3cd0ed2826a7a15e97d0b8247202b8ffd9edaaef363f8f99","first_computed_at":"2026-05-18T02:51:41.427730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:41.427730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cuBfwF5u6dNXujQeQWpivwkDz8IQC41bUbtpjVuwVI0dDK4Ll270KGpw78U5CFPJZQA4kcrSCUhIjufxxMy/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:41.428220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38aae9a80385d7fcbcd9c07b535a15adfc0874ecb2467bb7878fb20d5d40477b","sha256:61fceab1b8ad02ee04293bcbb66d4441a3c0f15420293618899cfabc5238d3c9"],"state_sha256":"e51851902cc7300863c0dac1866e51ce64071fee1b596a6bd2970e04cb381bc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MxvV2qgQU4k+kFpL9HDPlzYl9OC20IARZ1ikdBaHjDWXjCMFUEKAkMlHHcLrd1CzACjVfdkT6g5fPX8BlkltAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:48:10.850782Z","bundle_sha256":"de05748997bcd6adda0c1c7a072f9763e8d24507cb453073e0a969c69191e996"}}