{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MGLA2ZEP32ZSNXL7AIWD4VE24O","short_pith_number":"pith:MGLA2ZEP","canonical_record":{"source":{"id":"1809.09581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-09-25T16:40:44Z","cross_cats_sorted":[],"title_canon_sha256":"9a0af4fc56b60425c6270cab7f1dd14c386560f9dc9fb1510b21d6d18b4e63e3","abstract_canon_sha256":"fd335a0b6b270c35abe3b0e41491e3812045eff01893a31a187f74ee5d1be5cc"},"schema_version":"1.0"},"canonical_sha256":"61960d648fdeb326dd7f022c3e549ae3a608c2abfd64e179a40031400382845b","source":{"kind":"arxiv","id":"1809.09581","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09581","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09581v2","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09581","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"MGLA2ZEP32ZS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MGLA2ZEP32ZSNXL7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MGLA2ZEP","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MGLA2ZEP32ZSNXL7AIWD4VE24O","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-09-25T16:40:44Z","cross_cats_sorted":[],"title_canon_sha256":"9a0af4fc56b60425c6270cab7f1dd14c386560f9dc9fb1510b21d6d18b4e63e3","abstract_canon_sha256":"fd335a0b6b270c35abe3b0e41491e3812045eff01893a31a187f74ee5d1be5cc"},"schema_version":"1.0"},"canonical_sha256":"61960d648fdeb326dd7f022c3e549ae3a608c2abfd64e179a40031400382845b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:27.059331Z","signature_b64":"Iqv0jp9yqvC8qFYMbCWurkBgIv7LzNR+HRG35w/W9mwK2ILJoJeGst5lkWHuIfBXnYv3DhtPPeT9l17Oy5t0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61960d648fdeb326dd7f022c3e549ae3a608c2abfd64e179a40031400382845b","last_reissued_at":"2026-05-17T23:39:27.058788Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:27.058788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09581","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":"2026-05-17T23:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Og0UpmZGQu/jiXmErsjRmXFHx+RVQ0zrC3X1nlvSGXsJVesq0WHl65gwgbA9DAylf7Y/lj5exAH//qc2l8pICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:35:03.864533Z"},"content_sha256":"be321d53d07e4999687a8cc3422c65ef3c4db52ffa80608f0abd002f8454d997","schema_version":"1.0","event_id":"sha256:be321d53d07e4999687a8cc3422c65ef3c4db52ffa80608f0abd002f8454d997"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MGLA2ZEP32ZSNXL7AIWD4VE24O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dispersion relations of periodic quantum graphs associated with Archimedean tiling (I)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Chun-Kong Law, Eduardo O. Jatulan, Yu-Chen Luo","submitted_at":"2018-09-25T16:40:44Z","abstract_excerpt":"There are totally 11 kinds of Archimedean tiling for the plane. Applying the Floquet-Bloch theory, we derive the dispersion relations of the periodic quantum graphs associated with a number of Archimedean tiling, namely the triangular tiling {$(3^6)$}, the elongated triangular tiling {$(3^3,4^2)$}, the trihexagonal tiling {$(3,6,3,6)$} and the truncated square tiling {$(4,8^2)$}. The derivation makes use of characteristic functions, with the help of the symbolic software Mathematica.\n  The resulting dispersion relations are surprisingly simple and symmetric. They show that in each case the spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09581","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":"2026-05-17T23:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjK/muSZVTdfk1G0DkeLto35Vy2DR98TdvGQ9E1NOZpJ5z4BjFlkHYl9img7PK1uWOl34Mprh5X0bQOHwDPUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:35:03.864881Z"},"content_sha256":"0f02e6b04fc28ade7c23e0b1365898ec7115f55c86417d649056607fdf94042b","schema_version":"1.0","event_id":"sha256:0f02e6b04fc28ade7c23e0b1365898ec7115f55c86417d649056607fdf94042b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGLA2ZEP32ZSNXL7AIWD4VE24O/bundle.json","state_url":"https://pith.science/pith/MGLA2ZEP32ZSNXL7AIWD4VE24O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGLA2ZEP32ZSNXL7AIWD4VE24O/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":"2026-05-30T23:35:03Z","links":{"resolver":"https://pith.science/pith/MGLA2ZEP32ZSNXL7AIWD4VE24O","bundle":"https://pith.science/pith/MGLA2ZEP32ZSNXL7AIWD4VE24O/bundle.json","state":"https://pith.science/pith/MGLA2ZEP32ZSNXL7AIWD4VE24O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGLA2ZEP32ZSNXL7AIWD4VE24O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MGLA2ZEP32ZSNXL7AIWD4VE24O","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":"fd335a0b6b270c35abe3b0e41491e3812045eff01893a31a187f74ee5d1be5cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-09-25T16:40:44Z","title_canon_sha256":"9a0af4fc56b60425c6270cab7f1dd14c386560f9dc9fb1510b21d6d18b4e63e3"},"schema_version":"1.0","source":{"id":"1809.09581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09581","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09581v2","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09581","created_at":"2026-05-17T23:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"MGLA2ZEP32ZS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MGLA2ZEP32ZSNXL7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MGLA2ZEP","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:0f02e6b04fc28ade7c23e0b1365898ec7115f55c86417d649056607fdf94042b","target":"graph","created_at":"2026-05-17T23:39:27Z","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":"There are totally 11 kinds of Archimedean tiling for the plane. Applying the Floquet-Bloch theory, we derive the dispersion relations of the periodic quantum graphs associated with a number of Archimedean tiling, namely the triangular tiling {$(3^6)$}, the elongated triangular tiling {$(3^3,4^2)$}, the trihexagonal tiling {$(3,6,3,6)$} and the truncated square tiling {$(4,8^2)$}. The derivation makes use of characteristic functions, with the help of the symbolic software Mathematica.\n  The resulting dispersion relations are surprisingly simple and symmetric. They show that in each case the spe","authors_text":"Chun-Kong Law, Eduardo O. Jatulan, Yu-Chen Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-09-25T16:40:44Z","title":"Dispersion relations of periodic quantum graphs associated with Archimedean tiling (I)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09581","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:be321d53d07e4999687a8cc3422c65ef3c4db52ffa80608f0abd002f8454d997","target":"record","created_at":"2026-05-17T23:39:27Z","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":"fd335a0b6b270c35abe3b0e41491e3812045eff01893a31a187f74ee5d1be5cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-09-25T16:40:44Z","title_canon_sha256":"9a0af4fc56b60425c6270cab7f1dd14c386560f9dc9fb1510b21d6d18b4e63e3"},"schema_version":"1.0","source":{"id":"1809.09581","kind":"arxiv","version":2}},"canonical_sha256":"61960d648fdeb326dd7f022c3e549ae3a608c2abfd64e179a40031400382845b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61960d648fdeb326dd7f022c3e549ae3a608c2abfd64e179a40031400382845b","first_computed_at":"2026-05-17T23:39:27.058788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:27.058788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Iqv0jp9yqvC8qFYMbCWurkBgIv7LzNR+HRG35w/W9mwK2ILJoJeGst5lkWHuIfBXnYv3DhtPPeT9l17Oy5t0CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:27.059331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be321d53d07e4999687a8cc3422c65ef3c4db52ffa80608f0abd002f8454d997","sha256:0f02e6b04fc28ade7c23e0b1365898ec7115f55c86417d649056607fdf94042b"],"state_sha256":"0ebe8d6ce8a04d851d5d50890ec66c421fd63d06f6cb267bdc29ee50ddfd469f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1lhIEqH+Dt9tLGCBnkiJ67t2oTWXQySvxtV5aG9PivXuR1a5lqIO/R+Svb58Y/2FPO5utJzvigYFlRf7u08KCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:35:03.866850Z","bundle_sha256":"003303d254e155ab6409c62dc400747b85f984a95204d5ac45b37dc45340c00d"}}