{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:JM6UYDJM7U7QNFUPOQ23ECGTZP","short_pith_number":"pith:JM6UYDJM","canonical_record":{"source":{"id":"chao-dyn/9509019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1995-09-26T16:15:38Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"59b1167aa7f5f5030ac6e1fff31186af950964b6814ad5711ed762b468a0af19","abstract_canon_sha256":"3b022752431b5fe6033bfa7268730443a8c27e2fa23ccfe87a51c04b66b4503b"},"schema_version":"1.0"},"canonical_sha256":"4b3d4c0d2cfd3f06968f7435b208d3cbf0063742ebfbeea5ae034e4709bb481f","source":{"kind":"arxiv","id":"chao-dyn/9509019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9509019","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9509019v1","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9509019","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"JM6UYDJM7U7Q","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"JM6UYDJM7U7QNFUP","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"JM6UYDJM","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:JM6UYDJM7U7QNFUPOQ23ECGTZP","target":"record","payload":{"canonical_record":{"source":{"id":"chao-dyn/9509019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1995-09-26T16:15:38Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"59b1167aa7f5f5030ac6e1fff31186af950964b6814ad5711ed762b468a0af19","abstract_canon_sha256":"3b022752431b5fe6033bfa7268730443a8c27e2fa23ccfe87a51c04b66b4503b"},"schema_version":"1.0"},"canonical_sha256":"4b3d4c0d2cfd3f06968f7435b208d3cbf0063742ebfbeea5ae034e4709bb481f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:21.218894Z","signature_b64":"u7GsxSKsJ4K6q34ZqODOel3JgVzBlSbtgdsutKaR+d1VSYfBJtwxXrLNRh/dDhS/TLcBV7vhi3pOakULnF9CAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b3d4c0d2cfd3f06968f7435b208d3cbf0063742ebfbeea5ae034e4709bb481f","last_reissued_at":"2026-05-18T01:09:21.218449Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:21.218449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"chao-dyn/9509019","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":"2026-05-18T01:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KmgMsE90JikFkHSh9NFQDu0fAgHWjizoNSlZ+gYhfOD41e3P/fLQMcvVImlbxmgP86hpH4NWGqLqXfqoxdg8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:04:49.226390Z"},"content_sha256":"167a38e59d2f203f5e644171ffb781c88b80e6a2b3cd5e3f696ef99a426799e8","schema_version":"1.0","event_id":"sha256:167a38e59d2f203f5e644171ffb781c88b80e6a2b3cd5e3f696ef99a426799e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:JM6UYDJM7U7QNFUPOQ23ECGTZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of Eigenvalues for the Modular Group","license":"","headline":"","cross_cats":["nlin.CD"],"primary_cat":"chao-dyn","authors_text":"C. Schmit (Division de Physique Th\\'eorique, E. Bogomolny (Division de Physique Th\\'eorique, F. Leyvraz (Instituto de F\\'isica, France), Institut de Physique Nucl\\'eaire, Mexico City), Orsay, University of Mexico","submitted_at":"1995-09-26T16:15:38Z","abstract_excerpt":"The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that ion the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9509019","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":"2026-05-18T01:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V1m+zPmmXq9xhXZiEX79RJDfaMLHrPNhoKVjfxEIjR8rrpgJ0P9nDztvZgvskfAav/3ydJupy9xqEo4USg30BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:04:49.227091Z"},"content_sha256":"aef1809fe029c980d063a36d7fc3fef7ceef347de852e80604178dc9d8bcc825","schema_version":"1.0","event_id":"sha256:aef1809fe029c980d063a36d7fc3fef7ceef347de852e80604178dc9d8bcc825"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JM6UYDJM7U7QNFUPOQ23ECGTZP/bundle.json","state_url":"https://pith.science/pith/JM6UYDJM7U7QNFUPOQ23ECGTZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JM6UYDJM7U7QNFUPOQ23ECGTZP/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":"2026-05-26T11:04:49Z","links":{"resolver":"https://pith.science/pith/JM6UYDJM7U7QNFUPOQ23ECGTZP","bundle":"https://pith.science/pith/JM6UYDJM7U7QNFUPOQ23ECGTZP/bundle.json","state":"https://pith.science/pith/JM6UYDJM7U7QNFUPOQ23ECGTZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JM6UYDJM7U7QNFUPOQ23ECGTZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:JM6UYDJM7U7QNFUPOQ23ECGTZP","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":"3b022752431b5fe6033bfa7268730443a8c27e2fa23ccfe87a51c04b66b4503b","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1995-09-26T16:15:38Z","title_canon_sha256":"59b1167aa7f5f5030ac6e1fff31186af950964b6814ad5711ed762b468a0af19"},"schema_version":"1.0","source":{"id":"chao-dyn/9509019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9509019","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9509019v1","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9509019","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"JM6UYDJM7U7Q","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"JM6UYDJM7U7QNFUP","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"JM6UYDJM","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:aef1809fe029c980d063a36d7fc3fef7ceef347de852e80604178dc9d8bcc825","target":"graph","created_at":"2026-05-18T01:09:21Z","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":"The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that ion the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations.","authors_text":"C. Schmit (Division de Physique Th\\'eorique, E. Bogomolny (Division de Physique Th\\'eorique, F. Leyvraz (Instituto de F\\'isica, France), Institut de Physique Nucl\\'eaire, Mexico City), Orsay, University of Mexico","cross_cats":["nlin.CD"],"headline":"","license":"","primary_cat":"chao-dyn","submitted_at":"1995-09-26T16:15:38Z","title":"Distribution of Eigenvalues for the Modular Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9509019","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":"sha256:167a38e59d2f203f5e644171ffb781c88b80e6a2b3cd5e3f696ef99a426799e8","target":"record","created_at":"2026-05-18T01:09:21Z","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":"3b022752431b5fe6033bfa7268730443a8c27e2fa23ccfe87a51c04b66b4503b","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1995-09-26T16:15:38Z","title_canon_sha256":"59b1167aa7f5f5030ac6e1fff31186af950964b6814ad5711ed762b468a0af19"},"schema_version":"1.0","source":{"id":"chao-dyn/9509019","kind":"arxiv","version":1}},"canonical_sha256":"4b3d4c0d2cfd3f06968f7435b208d3cbf0063742ebfbeea5ae034e4709bb481f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b3d4c0d2cfd3f06968f7435b208d3cbf0063742ebfbeea5ae034e4709bb481f","first_computed_at":"2026-05-18T01:09:21.218449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:21.218449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u7GsxSKsJ4K6q34ZqODOel3JgVzBlSbtgdsutKaR+d1VSYfBJtwxXrLNRh/dDhS/TLcBV7vhi3pOakULnF9CAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:21.218894Z","signed_message":"canonical_sha256_bytes"},"source_id":"chao-dyn/9509019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:167a38e59d2f203f5e644171ffb781c88b80e6a2b3cd5e3f696ef99a426799e8","sha256:aef1809fe029c980d063a36d7fc3fef7ceef347de852e80604178dc9d8bcc825"],"state_sha256":"2fbd80d498f6156162b352d6c04943e4c0fbeddd9bf55e49884fd35e002559b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m3t3FazbmQbWXbTGJS5SlNllj0zp/xnB/GxL8oAVEufpcnsgKoUn/U1O5DnGmFCSJZmR2NKZeZ7tpxKBxifEDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:04:49.230611Z","bundle_sha256":"777f658cbacde0370e33e6fa13b3dc442e4f5ad31cba883bae97def3eb89d5e8"}}