{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3F7S5HBOIUY2AA7UFL32RWK7ZS","short_pith_number":"pith:3F7S5HBO","canonical_record":{"source":{"id":"1102.1304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-07T13:50:38Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"1e5c30166c1f660f12dfe839db7ef38305c362ff4b623550c6e5f1d5de57fd36","abstract_canon_sha256":"920ddcea6d32cc649e285c72ed771ba16926ca6a25b8e1826a365cfbef27b429"},"schema_version":"1.0"},"canonical_sha256":"d97f2e9c2e4531a003f42af7a8d95fccb9fa8aab9eda881a1859b8fc90c02c8b","source":{"kind":"arxiv","id":"1102.1304","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1304","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1304v1","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1304","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"3F7S5HBOIUY2","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3F7S5HBOIUY2AA7U","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3F7S5HBO","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3F7S5HBOIUY2AA7UFL32RWK7ZS","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-07T13:50:38Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"1e5c30166c1f660f12dfe839db7ef38305c362ff4b623550c6e5f1d5de57fd36","abstract_canon_sha256":"920ddcea6d32cc649e285c72ed771ba16926ca6a25b8e1826a365cfbef27b429"},"schema_version":"1.0"},"canonical_sha256":"d97f2e9c2e4531a003f42af7a8d95fccb9fa8aab9eda881a1859b8fc90c02c8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:32.583998Z","signature_b64":"sKqsQwEP55NE6urd5XtBeOO99uCdo0uZ4uKzvuXTHpiPGPhdgxJsTd1kjYFuVZmlF/q8lkpSP8zDzrD5ZS0MBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d97f2e9c2e4531a003f42af7a8d95fccb9fa8aab9eda881a1859b8fc90c02c8b","last_reissued_at":"2026-05-18T04:26:32.583506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:32.583506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1304","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":"2026-05-18T04:26:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUT0CoJWXCURAQgesYRUZA1EeKHgZ64jkV/2JrR2kxscNWAKydI6SiqDJ3shv7fCry6Lm+VCkaSFQFpCKZ/1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:36:07.952284Z"},"content_sha256":"b8644b9f7247bc3d8b6ba05c5c4c7dbea744cbd4b9f34465b429655bf6de0ccb","schema_version":"1.0","event_id":"sha256:b8644b9f7247bc3d8b6ba05c5c4c7dbea744cbd4b9f34465b429655bf6de0ccb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3F7S5HBOIUY2AA7UFL32RWK7ZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Zeta Function and Gauge Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Yang-Hui He","submitted_at":"2011-02-07T13:50:38Z","abstract_excerpt":"Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of quiver theories and periodic tilings by bi-partite graphs. In particular, we examine issues such as the spectra of the adjacency and whether the gauge theory satisfies the strong and weak versions of the graph theoretical analogue of the Riemann Hypothesis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1304","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":"2026-05-18T04:26:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZBNVlEF/hYYIQSSzKH8qO/Co3TwHn7tyS+k0MEXXyeCdteked+Ac+mngHRvY2jRiW5ZmGKgNNoaiKHDPEEqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:36:07.952785Z"},"content_sha256":"8a4c7492b23a8c14d186ad7e48e0ba8ca8a7c2e8ae33558064cba21b19d90899","schema_version":"1.0","event_id":"sha256:8a4c7492b23a8c14d186ad7e48e0ba8ca8a7c2e8ae33558064cba21b19d90899"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3F7S5HBOIUY2AA7UFL32RWK7ZS/bundle.json","state_url":"https://pith.science/pith/3F7S5HBOIUY2AA7UFL32RWK7ZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3F7S5HBOIUY2AA7UFL32RWK7ZS/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":"2026-05-26T11:36:07Z","links":{"resolver":"https://pith.science/pith/3F7S5HBOIUY2AA7UFL32RWK7ZS","bundle":"https://pith.science/pith/3F7S5HBOIUY2AA7UFL32RWK7ZS/bundle.json","state":"https://pith.science/pith/3F7S5HBOIUY2AA7UFL32RWK7ZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3F7S5HBOIUY2AA7UFL32RWK7ZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3F7S5HBOIUY2AA7UFL32RWK7ZS","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":"920ddcea6d32cc649e285c72ed771ba16926ca6a25b8e1826a365cfbef27b429","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-07T13:50:38Z","title_canon_sha256":"1e5c30166c1f660f12dfe839db7ef38305c362ff4b623550c6e5f1d5de57fd36"},"schema_version":"1.0","source":{"id":"1102.1304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1304","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1304v1","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1304","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"3F7S5HBOIUY2","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3F7S5HBOIUY2AA7U","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3F7S5HBO","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:8a4c7492b23a8c14d186ad7e48e0ba8ca8a7c2e8ae33558064cba21b19d90899","target":"graph","created_at":"2026-05-18T04:26:32Z","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":"Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of quiver theories and periodic tilings by bi-partite graphs. In particular, we examine issues such as the spectra of the adjacency and whether the gauge theory satisfies the strong and weak versions of the graph theoretical analogue of the Riemann Hypothesis.","authors_text":"Yang-Hui He","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-07T13:50:38Z","title":"Graph Zeta Function and Gauge Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1304","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:b8644b9f7247bc3d8b6ba05c5c4c7dbea744cbd4b9f34465b429655bf6de0ccb","target":"record","created_at":"2026-05-18T04:26:32Z","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":"920ddcea6d32cc649e285c72ed771ba16926ca6a25b8e1826a365cfbef27b429","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-02-07T13:50:38Z","title_canon_sha256":"1e5c30166c1f660f12dfe839db7ef38305c362ff4b623550c6e5f1d5de57fd36"},"schema_version":"1.0","source":{"id":"1102.1304","kind":"arxiv","version":1}},"canonical_sha256":"d97f2e9c2e4531a003f42af7a8d95fccb9fa8aab9eda881a1859b8fc90c02c8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d97f2e9c2e4531a003f42af7a8d95fccb9fa8aab9eda881a1859b8fc90c02c8b","first_computed_at":"2026-05-18T04:26:32.583506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:32.583506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sKqsQwEP55NE6urd5XtBeOO99uCdo0uZ4uKzvuXTHpiPGPhdgxJsTd1kjYFuVZmlF/q8lkpSP8zDzrD5ZS0MBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:32.583998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8644b9f7247bc3d8b6ba05c5c4c7dbea744cbd4b9f34465b429655bf6de0ccb","sha256:8a4c7492b23a8c14d186ad7e48e0ba8ca8a7c2e8ae33558064cba21b19d90899"],"state_sha256":"e6db058d609f760ca6a99541b51fb328acdb2e1bf2965bc0b3cb1c497788b926"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4dSh1UTs6+TE9hj9AV4EoTr9XpKsSX+cyH4i9tor6AUfdnpEFOzLkxyGXzP7cmUqoZu8eKgpoZQUixDgq51DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:36:07.956018Z","bundle_sha256":"a8d1aeebf4cb38d7149e643aed1be65b3fdb23bb8db65acc61b681997e4d6b71"}}