{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:C7GCQKJYLDFCK2UU4FTIWFEHCC","short_pith_number":"pith:C7GCQKJY","canonical_record":{"source":{"id":"1407.1148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-07-04T07:51:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"927b5ba16d51e3fea4ed5957327c7400fe2be64e2ebe923f7aaf8a739cb2d672","abstract_canon_sha256":"b3533d49ba0e5ebb47387f4de9b7f7c492550e2427d06890b7ba64c9e942209e"},"schema_version":"1.0"},"canonical_sha256":"17cc28293858ca256a94e1668b1487108abf2cd2a8462530d3e6f05c66205bb2","source":{"kind":"arxiv","id":"1407.1148","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1148","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1148v2","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1148","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"C7GCQKJYLDFC","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C7GCQKJYLDFCK2UU","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C7GCQKJY","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:C7GCQKJYLDFCK2UU4FTIWFEHCC","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-07-04T07:51:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"927b5ba16d51e3fea4ed5957327c7400fe2be64e2ebe923f7aaf8a739cb2d672","abstract_canon_sha256":"b3533d49ba0e5ebb47387f4de9b7f7c492550e2427d06890b7ba64c9e942209e"},"schema_version":"1.0"},"canonical_sha256":"17cc28293858ca256a94e1668b1487108abf2cd2a8462530d3e6f05c66205bb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:26.447334Z","signature_b64":"G6eEgBA69Mm2Zv5NCiuiCGIvlcvEDJ1PAyshMkKbZ+NFGt+7CKug0zVPUa9l9fCFhhBE0phbEjPbH/ixzGmYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17cc28293858ca256a94e1668b1487108abf2cd2a8462530d3e6f05c66205bb2","last_reissued_at":"2026-05-18T02:25:26.446788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:26.446788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1148","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRBB8Oii7i2ch9xXxM9S4niE6ET9Vnn2TE1H+FFgXMvNwatb0YPaEJ4s20bJMY81CD2TedX+drvG/o9h5OC0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:17:40.533302Z"},"content_sha256":"800da45f9997b18285106acebc5b4155166af39dfb48bfbce2560e948b953240","schema_version":"1.0","event_id":"sha256:800da45f9997b18285106acebc5b4155166af39dfb48bfbce2560e948b953240"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:C7GCQKJYLDFCK2UU4FTIWFEHCC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Graphs and Random-Matrix Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.CD","authors_text":"H. A. Weidenm\\\"uller, Z. Pluhar","submitted_at":"2014-07-04T07:51:20Z","abstract_excerpt":"For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P, Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We use that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1148","kind":"arxiv","version":2},"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":"2026-05-18T02:25:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rUiUrK7x7Bw+CKkOBZsCcKu34xk/I7EJwRS1YFnZZp65K421MwGMcZxTWPq4OwMOU+CRxYUjqAMcPg09SW/qCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:17:40.533684Z"},"content_sha256":"c7f7d58e932c86a182f69010629d414d58b6f35cb9d2febec917ecdb083d5191","schema_version":"1.0","event_id":"sha256:c7f7d58e932c86a182f69010629d414d58b6f35cb9d2febec917ecdb083d5191"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C7GCQKJYLDFCK2UU4FTIWFEHCC/bundle.json","state_url":"https://pith.science/pith/C7GCQKJYLDFCK2UU4FTIWFEHCC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C7GCQKJYLDFCK2UU4FTIWFEHCC/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":"2026-06-02T01:17:40Z","links":{"resolver":"https://pith.science/pith/C7GCQKJYLDFCK2UU4FTIWFEHCC","bundle":"https://pith.science/pith/C7GCQKJYLDFCK2UU4FTIWFEHCC/bundle.json","state":"https://pith.science/pith/C7GCQKJYLDFCK2UU4FTIWFEHCC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C7GCQKJYLDFCK2UU4FTIWFEHCC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C7GCQKJYLDFCK2UU4FTIWFEHCC","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":"b3533d49ba0e5ebb47387f4de9b7f7c492550e2427d06890b7ba64c9e942209e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-07-04T07:51:20Z","title_canon_sha256":"927b5ba16d51e3fea4ed5957327c7400fe2be64e2ebe923f7aaf8a739cb2d672"},"schema_version":"1.0","source":{"id":"1407.1148","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1148","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1148v2","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1148","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"C7GCQKJYLDFC","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C7GCQKJYLDFCK2UU","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C7GCQKJY","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:c7f7d58e932c86a182f69010629d414d58b6f35cb9d2febec917ecdb083d5191","target":"graph","created_at":"2026-05-18T02:25:26Z","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":"For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P, Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We use that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective","authors_text":"H. A. Weidenm\\\"uller, Z. Pluhar","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-07-04T07:51:20Z","title":"Quantum Graphs and Random-Matrix Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1148","kind":"arxiv","version":2},"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":"sha256:800da45f9997b18285106acebc5b4155166af39dfb48bfbce2560e948b953240","target":"record","created_at":"2026-05-18T02:25:26Z","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":"b3533d49ba0e5ebb47387f4de9b7f7c492550e2427d06890b7ba64c9e942209e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-07-04T07:51:20Z","title_canon_sha256":"927b5ba16d51e3fea4ed5957327c7400fe2be64e2ebe923f7aaf8a739cb2d672"},"schema_version":"1.0","source":{"id":"1407.1148","kind":"arxiv","version":2}},"canonical_sha256":"17cc28293858ca256a94e1668b1487108abf2cd2a8462530d3e6f05c66205bb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17cc28293858ca256a94e1668b1487108abf2cd2a8462530d3e6f05c66205bb2","first_computed_at":"2026-05-18T02:25:26.446788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:26.446788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G6eEgBA69Mm2Zv5NCiuiCGIvlcvEDJ1PAyshMkKbZ+NFGt+7CKug0zVPUa9l9fCFhhBE0phbEjPbH/ixzGmYBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:26.447334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1148","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:800da45f9997b18285106acebc5b4155166af39dfb48bfbce2560e948b953240","sha256:c7f7d58e932c86a182f69010629d414d58b6f35cb9d2febec917ecdb083d5191"],"state_sha256":"d72bc5cc44b330fe9e43042039a1ffbc9d20d9d0e79d3757ff7931e7abd15933"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGfBJ9vAEGBs9cDqJOvy5ZCOwrPSW7pMhqWWQS1iXey3vWWYOx7oqVdTOaoNImqyypVtWYXb3k1n9pZXlkhDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:17:40.535694Z","bundle_sha256":"95869c5f0d23f191f8f0e09e0c7b72d44061e63a8aeacaec017ba2acbb18a568"}}