{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NOM5ZKS75GNDIR5HEUVU2S2TYP","short_pith_number":"pith:NOM5ZKS7","canonical_record":{"source":{"id":"1807.05719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-16T08:17:25Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3e70ed6e15b0e0fe04f57a5d5af3697459a1794eeaadce9974b8dac0beee2f04","abstract_canon_sha256":"8df6d02c3da1cc47654395f5367bfa9265964fab32483cdee26e4302e043103b"},"schema_version":"1.0"},"canonical_sha256":"6b99dcaa5fe99a3447a7252b4d4b53c3ded3bb9e3d76bc14d7437fe0d35bf6e8","source":{"kind":"arxiv","id":"1807.05719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05719","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05719v1","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05719","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"NOM5ZKS75GND","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NOM5ZKS75GNDIR5H","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NOM5ZKS7","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NOM5ZKS75GNDIR5HEUVU2S2TYP","target":"record","payload":{"canonical_record":{"source":{"id":"1807.05719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-16T08:17:25Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3e70ed6e15b0e0fe04f57a5d5af3697459a1794eeaadce9974b8dac0beee2f04","abstract_canon_sha256":"8df6d02c3da1cc47654395f5367bfa9265964fab32483cdee26e4302e043103b"},"schema_version":"1.0"},"canonical_sha256":"6b99dcaa5fe99a3447a7252b4d4b53c3ded3bb9e3d76bc14d7437fe0d35bf6e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:42.768359Z","signature_b64":"NpgIv3EeZZQE/EaefISV01W1I294lAP8JlQzyeiHzpddwS1cJHGmFpg7FG4LU9lVWMrfDS12FCHIumzumFoJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b99dcaa5fe99a3447a7252b4d4b53c3ded3bb9e3d76bc14d7437fe0d35bf6e8","last_reissued_at":"2026-05-18T00:10:42.767655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:42.767655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.05719","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":"2026-05-18T00:10:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0/DIpWHXJ//1kBudiynmg9h9i59oGkm1l1Ox6+R1iERlsGi1YcCsdsWIBTQPwVatmFSRc63xyMPA1UGHsXIIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:43:27.410074Z"},"content_sha256":"735e52f77374a6da7d2491d5b08c3924a70054084b12e62125b5ec6aacc28e0b","schema_version":"1.0","event_id":"sha256:735e52f77374a6da7d2491d5b08c3924a70054084b12e62125b5ec6aacc28e0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NOM5ZKS75GNDIR5HEUVU2S2TYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sur certaines \\'equations fonctionnelles approch\\'ees, li\\'ees \\`a la transformation de Gauss","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Bruno Martin (LMPA), Michel Balazard (I2M)","submitted_at":"2018-07-16T08:17:25Z","abstract_excerpt":"In the line of classical work by Hardy, Littlewood and Wilton, we study a class of functional equations involving the Gauss transformation from the theory of continued fractions. This allows us to reprove, among others, a convergence criterion for a diophantine series considered by Chowla, and to give additional information about the sum of this series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05719","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":"2026-05-18T00:10:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vX7jmXv/BR0hwrGSnaIWKTa2fvA8XwZENaogKwIbjVuZF5uLKG14gheU615eh+mY/2cOPUXESHA8Xqjuw3p+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:43:27.410435Z"},"content_sha256":"0efd296a9130bad0c1dc50257bcb53ff1e6f13549668e69f6a0c2a12b2cf1d70","schema_version":"1.0","event_id":"sha256:0efd296a9130bad0c1dc50257bcb53ff1e6f13549668e69f6a0c2a12b2cf1d70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOM5ZKS75GNDIR5HEUVU2S2TYP/bundle.json","state_url":"https://pith.science/pith/NOM5ZKS75GNDIR5HEUVU2S2TYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOM5ZKS75GNDIR5HEUVU2S2TYP/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":"2026-06-26T12:43:27Z","links":{"resolver":"https://pith.science/pith/NOM5ZKS75GNDIR5HEUVU2S2TYP","bundle":"https://pith.science/pith/NOM5ZKS75GNDIR5HEUVU2S2TYP/bundle.json","state":"https://pith.science/pith/NOM5ZKS75GNDIR5HEUVU2S2TYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOM5ZKS75GNDIR5HEUVU2S2TYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NOM5ZKS75GNDIR5HEUVU2S2TYP","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":"8df6d02c3da1cc47654395f5367bfa9265964fab32483cdee26e4302e043103b","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-16T08:17:25Z","title_canon_sha256":"3e70ed6e15b0e0fe04f57a5d5af3697459a1794eeaadce9974b8dac0beee2f04"},"schema_version":"1.0","source":{"id":"1807.05719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05719","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05719v1","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05719","created_at":"2026-05-18T00:10:42Z"},{"alias_kind":"pith_short_12","alias_value":"NOM5ZKS75GND","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NOM5ZKS75GNDIR5H","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NOM5ZKS7","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:0efd296a9130bad0c1dc50257bcb53ff1e6f13549668e69f6a0c2a12b2cf1d70","target":"graph","created_at":"2026-05-18T00:10:42Z","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":"In the line of classical work by Hardy, Littlewood and Wilton, we study a class of functional equations involving the Gauss transformation from the theory of continued fractions. This allows us to reprove, among others, a convergence criterion for a diophantine series considered by Chowla, and to give additional information about the sum of this series.","authors_text":"Bruno Martin (LMPA), Michel Balazard (I2M)","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-16T08:17:25Z","title":"Sur certaines \\'equations fonctionnelles approch\\'ees, li\\'ees \\`a la transformation de Gauss"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05719","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":"sha256:735e52f77374a6da7d2491d5b08c3924a70054084b12e62125b5ec6aacc28e0b","target":"record","created_at":"2026-05-18T00:10:42Z","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":"8df6d02c3da1cc47654395f5367bfa9265964fab32483cdee26e4302e043103b","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-16T08:17:25Z","title_canon_sha256":"3e70ed6e15b0e0fe04f57a5d5af3697459a1794eeaadce9974b8dac0beee2f04"},"schema_version":"1.0","source":{"id":"1807.05719","kind":"arxiv","version":1}},"canonical_sha256":"6b99dcaa5fe99a3447a7252b4d4b53c3ded3bb9e3d76bc14d7437fe0d35bf6e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b99dcaa5fe99a3447a7252b4d4b53c3ded3bb9e3d76bc14d7437fe0d35bf6e8","first_computed_at":"2026-05-18T00:10:42.767655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:42.767655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NpgIv3EeZZQE/EaefISV01W1I294lAP8JlQzyeiHzpddwS1cJHGmFpg7FG4LU9lVWMrfDS12FCHIumzumFoJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:42.768359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.05719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:735e52f77374a6da7d2491d5b08c3924a70054084b12e62125b5ec6aacc28e0b","sha256:0efd296a9130bad0c1dc50257bcb53ff1e6f13549668e69f6a0c2a12b2cf1d70"],"state_sha256":"a54655ef2ec531bd7e7b33830977f9d7e6384c2af2ffc197d2e8d9b830cf7942"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LmgJ4YsVvYriO3bG2Z/v8nfcBKBk1mmhRx/rnTNZq8qRg2umC/pgQP9FbNTLl6C2q03w8b0fshQQs+vlmRn7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:43:27.412356Z","bundle_sha256":"02f852d825c84522ab569a53f730e92830701f66bb6b077a2164edd6f18a0b4b"}}