{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AMSDMVJU7IJU54TVPNOCX4RXOH","short_pith_number":"pith:AMSDMVJU","canonical_record":{"source":{"id":"1507.04176","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-15T11:48:35Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b31061e9c9957ad1eb147b177660b49b5474f032c5a61431566556baff13625c","abstract_canon_sha256":"2b9e3ef2aede4fbe942e173a3c1b02451ac3e35f1834fbb6d4fc0d7eb85c9933"},"schema_version":"1.0"},"canonical_sha256":"0324365534fa134ef2757b5c2bf23771dc9d2b28dbf872e80ab262b304bc837a","source":{"kind":"arxiv","id":"1507.04176","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04176","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04176v2","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04176","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"AMSDMVJU7IJU","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AMSDMVJU7IJU54TV","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AMSDMVJU","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AMSDMVJU7IJU54TVPNOCX4RXOH","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04176","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-15T11:48:35Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b31061e9c9957ad1eb147b177660b49b5474f032c5a61431566556baff13625c","abstract_canon_sha256":"2b9e3ef2aede4fbe942e173a3c1b02451ac3e35f1834fbb6d4fc0d7eb85c9933"},"schema_version":"1.0"},"canonical_sha256":"0324365534fa134ef2757b5c2bf23771dc9d2b28dbf872e80ab262b304bc837a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:14.548748Z","signature_b64":"x1ShmaXyAwnMNB9hkZiNUbPnb0oKoRtEJ8/XuMIGWZtUcg9um41jYGct3on0RLJsCBYdq997j9Y+4v3lcOp6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0324365534fa134ef2757b5c2bf23771dc9d2b28dbf872e80ab262b304bc837a","last_reissued_at":"2026-05-18T01:04:14.548365Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:14.548365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04176","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":"2026-05-18T01:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80IQ8WMB0XmvQnR4Q3JjXUl47x6s/DJt/Jcsx2JDlyc0f55uiOPbgcEv3A+V0ZbD4YNdn+K7zvZDpUKzU6TbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:24:19.898576Z"},"content_sha256":"ff65ff9fe2ee0617e3284549c915ffb9403a045e259619a83b640647b7eaf6cc","schema_version":"1.0","event_id":"sha256:ff65ff9fe2ee0617e3284549c915ffb9403a045e259619a83b640647b7eaf6cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AMSDMVJU7IJU54TVPNOCX4RXOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Effective Size of a Non-Weyl Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jiri Lipovsky","submitted_at":"2015-07-15T11:48:35Z","abstract_excerpt":"We show how to find the coefficient by the leading term of the resonance asymptotics using the method of pseudo orbit expansion for quantum graphs which do not obey the Weyl asymptotics. For a non-Weyl graph we develop a method how to reduce the number of edges of a corresponding directed graph. Through this method we prove bounds on the above coefficient depending on the structure of the graph for graphs with the same lengths of internal edges. We explicitly find the positions of the resolvent resonances."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04176","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":"2026-05-18T01:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ywNNJgnDHhD4XATCPsiz/tjKumedNjuwYnnCDFh6ki7oVmJ9ZaYOZpdsTr4ap5Vnwe5Wnb3OhRePYFp4o+QzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:24:19.898917Z"},"content_sha256":"d93c89d1f6f00d33ff6b08ca8d5eb46fca9a65668924d8d4d5c771f810318b71","schema_version":"1.0","event_id":"sha256:d93c89d1f6f00d33ff6b08ca8d5eb46fca9a65668924d8d4d5c771f810318b71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMSDMVJU7IJU54TVPNOCX4RXOH/bundle.json","state_url":"https://pith.science/pith/AMSDMVJU7IJU54TVPNOCX4RXOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMSDMVJU7IJU54TVPNOCX4RXOH/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":"2026-06-03T10:24:19Z","links":{"resolver":"https://pith.science/pith/AMSDMVJU7IJU54TVPNOCX4RXOH","bundle":"https://pith.science/pith/AMSDMVJU7IJU54TVPNOCX4RXOH/bundle.json","state":"https://pith.science/pith/AMSDMVJU7IJU54TVPNOCX4RXOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMSDMVJU7IJU54TVPNOCX4RXOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AMSDMVJU7IJU54TVPNOCX4RXOH","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":"2b9e3ef2aede4fbe942e173a3c1b02451ac3e35f1834fbb6d4fc0d7eb85c9933","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-15T11:48:35Z","title_canon_sha256":"b31061e9c9957ad1eb147b177660b49b5474f032c5a61431566556baff13625c"},"schema_version":"1.0","source":{"id":"1507.04176","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04176","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04176v2","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04176","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"AMSDMVJU7IJU","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AMSDMVJU7IJU54TV","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AMSDMVJU","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:d93c89d1f6f00d33ff6b08ca8d5eb46fca9a65668924d8d4d5c771f810318b71","target":"graph","created_at":"2026-05-18T01:04:14Z","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 show how to find the coefficient by the leading term of the resonance asymptotics using the method of pseudo orbit expansion for quantum graphs which do not obey the Weyl asymptotics. For a non-Weyl graph we develop a method how to reduce the number of edges of a corresponding directed graph. Through this method we prove bounds on the above coefficient depending on the structure of the graph for graphs with the same lengths of internal edges. We explicitly find the positions of the resolvent resonances.","authors_text":"Jiri Lipovsky","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-15T11:48:35Z","title":"On the Effective Size of a Non-Weyl Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04176","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:ff65ff9fe2ee0617e3284549c915ffb9403a045e259619a83b640647b7eaf6cc","target":"record","created_at":"2026-05-18T01:04:14Z","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":"2b9e3ef2aede4fbe942e173a3c1b02451ac3e35f1834fbb6d4fc0d7eb85c9933","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-15T11:48:35Z","title_canon_sha256":"b31061e9c9957ad1eb147b177660b49b5474f032c5a61431566556baff13625c"},"schema_version":"1.0","source":{"id":"1507.04176","kind":"arxiv","version":2}},"canonical_sha256":"0324365534fa134ef2757b5c2bf23771dc9d2b28dbf872e80ab262b304bc837a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0324365534fa134ef2757b5c2bf23771dc9d2b28dbf872e80ab262b304bc837a","first_computed_at":"2026-05-18T01:04:14.548365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:14.548365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x1ShmaXyAwnMNB9hkZiNUbPnb0oKoRtEJ8/XuMIGWZtUcg9um41jYGct3on0RLJsCBYdq997j9Y+4v3lcOp6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:14.548748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04176","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff65ff9fe2ee0617e3284549c915ffb9403a045e259619a83b640647b7eaf6cc","sha256:d93c89d1f6f00d33ff6b08ca8d5eb46fca9a65668924d8d4d5c771f810318b71"],"state_sha256":"441fc08cc85723fd4745f1ab6ae39f0cae161cf0716909f797aa7d4b58da48c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zCK/F7wFQWob47q6R/L7DIsWC0L+bYjM5yeyM9fCZxKttqMyOm5+EyAVhSB2kwIMFd1dj+CQDnPPikcbVwacCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:24:19.900852Z","bundle_sha256":"d49892dd4376549d863d959618d80b1f73e53b3afb91fe2c2ddc059cf9834d3c"}}