{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NPKR5SK3PH2E7UMLEF4ESFZRGR","short_pith_number":"pith:NPKR5SK3","canonical_record":{"source":{"id":"1201.0118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-12-30T12:49:14Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"0c0568b66f6192735729f479b687ff11a7ddfd8007291318f3849bee4cd78db7","abstract_canon_sha256":"e01a2ba6a395c81a906bec32d8768bef7b13f16eff7512716369baea78d2f0e0"},"schema_version":"1.0"},"canonical_sha256":"6bd51ec95b79f44fd18b2178491731346ef195d4ad8d4169f7b89aa248b7ee04","source":{"kind":"arxiv","id":"1201.0118","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0118","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0118v1","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0118","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"NPKR5SK3PH2E","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NPKR5SK3PH2E7UML","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NPKR5SK3","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NPKR5SK3PH2E7UMLEF4ESFZRGR","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-12-30T12:49:14Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"0c0568b66f6192735729f479b687ff11a7ddfd8007291318f3849bee4cd78db7","abstract_canon_sha256":"e01a2ba6a395c81a906bec32d8768bef7b13f16eff7512716369baea78d2f0e0"},"schema_version":"1.0"},"canonical_sha256":"6bd51ec95b79f44fd18b2178491731346ef195d4ad8d4169f7b89aa248b7ee04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:26.120768Z","signature_b64":"bMza+1qX2AduFf/1sBm38pLc62JfZ8EbEf1c2OHJThFCs51dk0qGrkKXFbHTc0/zaD4nr9+KASi4Zm0v0hE2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bd51ec95b79f44fd18b2178491731346ef195d4ad8d4169f7b89aa248b7ee04","last_reissued_at":"2026-05-18T04:05:26.120009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:26.120009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0118","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":"2026-05-18T04:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ZjCVCkKx7bTb4wom51eRSI/k0iQnsfJPqfAOO4G1gbs9a6gKo8r/aKmWUHlB0Tm1wa8JBsGybG8o9DecDK/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:49:06.939609Z"},"content_sha256":"f80111ba1c9e2cab349d40b79dde5e3fddf9369461f0786122f153edf82b1576","schema_version":"1.0","event_id":"sha256:f80111ba1c9e2cab349d40b79dde5e3fddf9369461f0786122f153edf82b1576"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NPKR5SK3PH2E7UMLEF4ESFZRGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Analysis of Certain Spherically Homogeneous Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Jonathan Breuer, Matthias Keller","submitted_at":"2011-12-30T12:49:14Z","abstract_excerpt":"We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the structure of the graph. Thus, the spectral properties of the adjacency matrix and the Laplacian can be analyzed by means of the elaborated theory of Jacobi matrices. For some examples which include antitrees, we derive the decomposition explicitly and present a zoo of spectral behavior induced by the geometry of the graph. In particular, these examples show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0118","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":"2026-05-18T04:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7fyrijTcFsAQdeo/Bcc+Py/qy2ZVP0TTxoAUKgcWHwarfmTr9QNRUFa2/fTvLOKam/mMG1U1TrE+4XG1TZzGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:49:06.940233Z"},"content_sha256":"e56e57ed603741c46339c2e604425aae0834d7ff11b048dfd152153525d94419","schema_version":"1.0","event_id":"sha256:e56e57ed603741c46339c2e604425aae0834d7ff11b048dfd152153525d94419"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPKR5SK3PH2E7UMLEF4ESFZRGR/bundle.json","state_url":"https://pith.science/pith/NPKR5SK3PH2E7UMLEF4ESFZRGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPKR5SK3PH2E7UMLEF4ESFZRGR/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":"2026-05-31T11:49:06Z","links":{"resolver":"https://pith.science/pith/NPKR5SK3PH2E7UMLEF4ESFZRGR","bundle":"https://pith.science/pith/NPKR5SK3PH2E7UMLEF4ESFZRGR/bundle.json","state":"https://pith.science/pith/NPKR5SK3PH2E7UMLEF4ESFZRGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPKR5SK3PH2E7UMLEF4ESFZRGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NPKR5SK3PH2E7UMLEF4ESFZRGR","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":"e01a2ba6a395c81a906bec32d8768bef7b13f16eff7512716369baea78d2f0e0","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-12-30T12:49:14Z","title_canon_sha256":"0c0568b66f6192735729f479b687ff11a7ddfd8007291318f3849bee4cd78db7"},"schema_version":"1.0","source":{"id":"1201.0118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0118","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0118v1","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0118","created_at":"2026-05-18T04:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"NPKR5SK3PH2E","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NPKR5SK3PH2E7UML","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NPKR5SK3","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:e56e57ed603741c46339c2e604425aae0834d7ff11b048dfd152153525d94419","target":"graph","created_at":"2026-05-18T04:05:26Z","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":"We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the structure of the graph. Thus, the spectral properties of the adjacency matrix and the Laplacian can be analyzed by means of the elaborated theory of Jacobi matrices. For some examples which include antitrees, we derive the decomposition explicitly and present a zoo of spectral behavior induced by the geometry of the graph. In particular, these examples show ","authors_text":"Jonathan Breuer, Matthias Keller","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-12-30T12:49:14Z","title":"Spectral Analysis of Certain Spherically Homogeneous Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0118","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:f80111ba1c9e2cab349d40b79dde5e3fddf9369461f0786122f153edf82b1576","target":"record","created_at":"2026-05-18T04:05:26Z","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":"e01a2ba6a395c81a906bec32d8768bef7b13f16eff7512716369baea78d2f0e0","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-12-30T12:49:14Z","title_canon_sha256":"0c0568b66f6192735729f479b687ff11a7ddfd8007291318f3849bee4cd78db7"},"schema_version":"1.0","source":{"id":"1201.0118","kind":"arxiv","version":1}},"canonical_sha256":"6bd51ec95b79f44fd18b2178491731346ef195d4ad8d4169f7b89aa248b7ee04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bd51ec95b79f44fd18b2178491731346ef195d4ad8d4169f7b89aa248b7ee04","first_computed_at":"2026-05-18T04:05:26.120009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:26.120009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bMza+1qX2AduFf/1sBm38pLc62JfZ8EbEf1c2OHJThFCs51dk0qGrkKXFbHTc0/zaD4nr9+KASi4Zm0v0hE2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:26.120768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f80111ba1c9e2cab349d40b79dde5e3fddf9369461f0786122f153edf82b1576","sha256:e56e57ed603741c46339c2e604425aae0834d7ff11b048dfd152153525d94419"],"state_sha256":"523bcddeb0d467daf5719fea4a525aa329cf145868522a9fb2c483da0e2159f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOnkJOEmDB0/FGhj6lN4PS78ZVFPv/B+/QRqE99ZnVxblk7ASjwOm5Qyxd8a9MjqY39JjydNUUj4h63yU7T9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:49:06.943771Z","bundle_sha256":"2cdfaccda9bb4fe6d870cfe0acbe4a347e907b870a467738552ad39d6526c0d1"}}