{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2AZRYS4NBSOERDT3JMTU5RY55H","short_pith_number":"pith:2AZRYS4N","canonical_record":{"source":{"id":"1401.5911","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-01-23T09:42:12Z","cross_cats_sorted":[],"title_canon_sha256":"8fc53881fd5aa9972eb9e7500a511682d543b3dc668b809b27ea55d3abe7d937","abstract_canon_sha256":"98dc7321f60aeca4a056a8cb10f913a43bc23ec93cde47ec7bb6bb7f92532ca4"},"schema_version":"1.0"},"canonical_sha256":"d0331c4b8d0c9c488e7b4b274ec71de9d90a74f2bed7cc5ea1f82843d00c1f87","source":{"kind":"arxiv","id":"1401.5911","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5911","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5911v2","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5911","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"2AZRYS4NBSOE","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2AZRYS4NBSOERDT3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2AZRYS4N","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2AZRYS4NBSOERDT3JMTU5RY55H","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5911","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-01-23T09:42:12Z","cross_cats_sorted":[],"title_canon_sha256":"8fc53881fd5aa9972eb9e7500a511682d543b3dc668b809b27ea55d3abe7d937","abstract_canon_sha256":"98dc7321f60aeca4a056a8cb10f913a43bc23ec93cde47ec7bb6bb7f92532ca4"},"schema_version":"1.0"},"canonical_sha256":"d0331c4b8d0c9c488e7b4b274ec71de9d90a74f2bed7cc5ea1f82843d00c1f87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:23.252664Z","signature_b64":"HYy/rhG8fOOC1vgZY7kOBipSHDpuqNa+WZOKIoLYGVI4D4eMzgTvXqkFNyj6r0JvQkwqZai/9/6KsT217SMMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0331c4b8d0c9c488e7b4b274ec71de9d90a74f2bed7cc5ea1f82843d00c1f87","last_reissued_at":"2026-05-18T02:52:23.251904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:23.251904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5911","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":"2026-05-18T02:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RTqoItxsG2LOBaaxXgYf4I9sAQlwFFbylUfg9Ew2NoZvj4ot83MBO26T48PbePeyZbA9RGXN6SBRHENQODYuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:58:10.261556Z"},"content_sha256":"7dbb15cf0238a8a7253ff4c22aab4feae7ab221277c9d4240d0dc36034dfd369","schema_version":"1.0","event_id":"sha256:7dbb15cf0238a8a7253ff4c22aab4feae7ab221277c9d4240d0dc36034dfd369"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2AZRYS4NBSOERDT3JMTU5RY55H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nodal domains of the equilateral triangle billiard","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Rhine Samajdar, Sudhir R. Jain","submitted_at":"2014-01-23T09:42:12Z","abstract_excerpt":"We characterise the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5911","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":"2026-05-18T02:52:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+IpioX70qHGcl8QTRd35eWapWUfcQWzlv+kWKEwDhOeD9u0gk1FZE8Ljpxn9P3+MIT/1bmzEl+dYQHzXo1LCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:58:10.262173Z"},"content_sha256":"d13a0a26ce40a713e62701707a51a225fd72a4d5e4f18437441a0fcc88dc6ab5","schema_version":"1.0","event_id":"sha256:d13a0a26ce40a713e62701707a51a225fd72a4d5e4f18437441a0fcc88dc6ab5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2AZRYS4NBSOERDT3JMTU5RY55H/bundle.json","state_url":"https://pith.science/pith/2AZRYS4NBSOERDT3JMTU5RY55H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2AZRYS4NBSOERDT3JMTU5RY55H/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":"2026-05-31T03:58:10Z","links":{"resolver":"https://pith.science/pith/2AZRYS4NBSOERDT3JMTU5RY55H","bundle":"https://pith.science/pith/2AZRYS4NBSOERDT3JMTU5RY55H/bundle.json","state":"https://pith.science/pith/2AZRYS4NBSOERDT3JMTU5RY55H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2AZRYS4NBSOERDT3JMTU5RY55H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2AZRYS4NBSOERDT3JMTU5RY55H","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":"98dc7321f60aeca4a056a8cb10f913a43bc23ec93cde47ec7bb6bb7f92532ca4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-01-23T09:42:12Z","title_canon_sha256":"8fc53881fd5aa9972eb9e7500a511682d543b3dc668b809b27ea55d3abe7d937"},"schema_version":"1.0","source":{"id":"1401.5911","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5911","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5911v2","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5911","created_at":"2026-05-18T02:52:23Z"},{"alias_kind":"pith_short_12","alias_value":"2AZRYS4NBSOE","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2AZRYS4NBSOERDT3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2AZRYS4N","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:d13a0a26ce40a713e62701707a51a225fd72a4d5e4f18437441a0fcc88dc6ab5","target":"graph","created_at":"2026-05-18T02:52:23Z","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 characterise the eigenfunctions of an equilateral triangle billiard in terms of its nodal domains. The number of nodal domains has a quadratic form in terms of the quantum numbers, with a non-trivial number-theoretic factor. The patterns of the eigenfunctions follow a group-theoretic connection in a way that makes them predictable as one goes from one state to another. Extensive numerical investigations bring out the distribution functions of the mode number and signed areas. The statistics of the boundary intersections is also treated analytically. Finally, the distribution functions of th","authors_text":"Rhine Samajdar, Sudhir R. Jain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-01-23T09:42:12Z","title":"Nodal domains of the equilateral triangle billiard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5911","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":"sha256:7dbb15cf0238a8a7253ff4c22aab4feae7ab221277c9d4240d0dc36034dfd369","target":"record","created_at":"2026-05-18T02:52:23Z","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":"98dc7321f60aeca4a056a8cb10f913a43bc23ec93cde47ec7bb6bb7f92532ca4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-01-23T09:42:12Z","title_canon_sha256":"8fc53881fd5aa9972eb9e7500a511682d543b3dc668b809b27ea55d3abe7d937"},"schema_version":"1.0","source":{"id":"1401.5911","kind":"arxiv","version":2}},"canonical_sha256":"d0331c4b8d0c9c488e7b4b274ec71de9d90a74f2bed7cc5ea1f82843d00c1f87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0331c4b8d0c9c488e7b4b274ec71de9d90a74f2bed7cc5ea1f82843d00c1f87","first_computed_at":"2026-05-18T02:52:23.251904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:23.251904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYy/rhG8fOOC1vgZY7kOBipSHDpuqNa+WZOKIoLYGVI4D4eMzgTvXqkFNyj6r0JvQkwqZai/9/6KsT217SMMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:23.252664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5911","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dbb15cf0238a8a7253ff4c22aab4feae7ab221277c9d4240d0dc36034dfd369","sha256:d13a0a26ce40a713e62701707a51a225fd72a4d5e4f18437441a0fcc88dc6ab5"],"state_sha256":"76dd24186a70ad028de6488698ca0ed3ace50e7245c0c95b1c112184166ea9d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gi2uvXkAR9kNHMiPr66bBfiTKRAIMUytBJooWgc3Ed8yKmhHOi/m8Kz8jyI781zu/1mPvv7HgRFXjbpTM5VNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:58:10.265419Z","bundle_sha256":"7f6b29b6bb80654bcd60b6c6e83458d67bb0287079130f828180fb9d92ef7ec7"}}