{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Q5NUH64GAK4TQKO7F4BQY4WA7Y","short_pith_number":"pith:Q5NUH64G","canonical_record":{"source":{"id":"1809.08765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-24T05:30:46Z","cross_cats_sorted":[],"title_canon_sha256":"5d7bae9fb558a0182a6ca31158a21e1a3ef059f35122609b84943a54811529f3","abstract_canon_sha256":"aa3da753ff5125cf7da8467918c57cab2dd2c29db561a7fb897f6e70eb4afb5e"},"schema_version":"1.0"},"canonical_sha256":"875b43fb8602b93829df2f030c72c0fe288d8c218f675bac8b118f284c438308","source":{"kind":"arxiv","id":"1809.08765","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08765","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08765v1","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08765","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"Q5NUH64GAK4T","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q5NUH64GAK4TQKO7","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q5NUH64G","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Q5NUH64GAK4TQKO7F4BQY4WA7Y","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-24T05:30:46Z","cross_cats_sorted":[],"title_canon_sha256":"5d7bae9fb558a0182a6ca31158a21e1a3ef059f35122609b84943a54811529f3","abstract_canon_sha256":"aa3da753ff5125cf7da8467918c57cab2dd2c29db561a7fb897f6e70eb4afb5e"},"schema_version":"1.0"},"canonical_sha256":"875b43fb8602b93829df2f030c72c0fe288d8c218f675bac8b118f284c438308","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:03.629247Z","signature_b64":"oIXt/tw+JbHHC+0aLWAgh95WNsbueIWtG4i1QTxUuDEVym4WntIaVHoRc3h/lJEuFkFvk7wZlgSIFNswwoJTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"875b43fb8602b93829df2f030c72c0fe288d8c218f675bac8b118f284c438308","last_reissued_at":"2026-05-18T00:05:03.628780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:03.628780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08765","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":"2026-05-18T00:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U4ZLeMQJYHQixV+h8R1l570/AC06I1F4N0X+31gcWlED7VFvbdtmn79ZqgR5wghmhU7Zc/insum/RtpljNboCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:42:37.043334Z"},"content_sha256":"74b46ea06115ee694ac87b1723c3eb792dc58a3f176383e3a092c05f4df239aa","schema_version":"1.0","event_id":"sha256:74b46ea06115ee694ac87b1723c3eb792dc58a3f176383e3a092c05f4df239aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Q5NUH64GAK4TQKO7F4BQY4WA7Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Asymptotics of the Laplacian on Surfaces of Constant Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Robert S. Strichartz, Timothy Murray","submitted_at":"2018-09-24T05:30:46Z","abstract_excerpt":"The purpose of this paper is to explore the asymptotics of the eigenvalue spectrum of the Laplacian on 2 dimensional spaces of constant curvature, giving strong experimental evidence for a conjecture of the second author \\cite{strichartz2016}. We computed and analyzed the eigenvalue spectra of several different regions in Euclidean, Hyperbolic, and Spherical space under Dirichlet, Neumann, and mixed boundary conditions and in particular we found that the average of the difference between the eigenvalue counting function and a 3-term prediction has the expected nice behavior. All computational "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08765","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":"2026-05-18T00:05:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2tOUnBOL8u6If7WPs7C6803XKLL0BUS4o9tT4baHxdgr3DkUhpU6SwOhX5i/c1Wr2bwQe+1XM1289s14ad3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:42:37.043695Z"},"content_sha256":"bad8fbb82c11529063e3fe37d35048906ce364187c52fc457d4032f82ff84782","schema_version":"1.0","event_id":"sha256:bad8fbb82c11529063e3fe37d35048906ce364187c52fc457d4032f82ff84782"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5NUH64GAK4TQKO7F4BQY4WA7Y/bundle.json","state_url":"https://pith.science/pith/Q5NUH64GAK4TQKO7F4BQY4WA7Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5NUH64GAK4TQKO7F4BQY4WA7Y/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":"2026-06-02T03:42:37Z","links":{"resolver":"https://pith.science/pith/Q5NUH64GAK4TQKO7F4BQY4WA7Y","bundle":"https://pith.science/pith/Q5NUH64GAK4TQKO7F4BQY4WA7Y/bundle.json","state":"https://pith.science/pith/Q5NUH64GAK4TQKO7F4BQY4WA7Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5NUH64GAK4TQKO7F4BQY4WA7Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q5NUH64GAK4TQKO7F4BQY4WA7Y","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":"aa3da753ff5125cf7da8467918c57cab2dd2c29db561a7fb897f6e70eb4afb5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-24T05:30:46Z","title_canon_sha256":"5d7bae9fb558a0182a6ca31158a21e1a3ef059f35122609b84943a54811529f3"},"schema_version":"1.0","source":{"id":"1809.08765","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08765","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08765v1","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08765","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"Q5NUH64GAK4T","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q5NUH64GAK4TQKO7","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q5NUH64G","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:bad8fbb82c11529063e3fe37d35048906ce364187c52fc457d4032f82ff84782","target":"graph","created_at":"2026-05-18T00:05:03Z","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":"The purpose of this paper is to explore the asymptotics of the eigenvalue spectrum of the Laplacian on 2 dimensional spaces of constant curvature, giving strong experimental evidence for a conjecture of the second author \\cite{strichartz2016}. We computed and analyzed the eigenvalue spectra of several different regions in Euclidean, Hyperbolic, and Spherical space under Dirichlet, Neumann, and mixed boundary conditions and in particular we found that the average of the difference between the eigenvalue counting function and a 3-term prediction has the expected nice behavior. All computational ","authors_text":"Robert S. Strichartz, Timothy Murray","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-24T05:30:46Z","title":"Spectral Asymptotics of the Laplacian on Surfaces of Constant Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08765","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":"sha256:74b46ea06115ee694ac87b1723c3eb792dc58a3f176383e3a092c05f4df239aa","target":"record","created_at":"2026-05-18T00:05:03Z","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":"aa3da753ff5125cf7da8467918c57cab2dd2c29db561a7fb897f6e70eb4afb5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-24T05:30:46Z","title_canon_sha256":"5d7bae9fb558a0182a6ca31158a21e1a3ef059f35122609b84943a54811529f3"},"schema_version":"1.0","source":{"id":"1809.08765","kind":"arxiv","version":1}},"canonical_sha256":"875b43fb8602b93829df2f030c72c0fe288d8c218f675bac8b118f284c438308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"875b43fb8602b93829df2f030c72c0fe288d8c218f675bac8b118f284c438308","first_computed_at":"2026-05-18T00:05:03.628780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:03.628780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oIXt/tw+JbHHC+0aLWAgh95WNsbueIWtG4i1QTxUuDEVym4WntIaVHoRc3h/lJEuFkFvk7wZlgSIFNswwoJTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:03.629247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08765","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74b46ea06115ee694ac87b1723c3eb792dc58a3f176383e3a092c05f4df239aa","sha256:bad8fbb82c11529063e3fe37d35048906ce364187c52fc457d4032f82ff84782"],"state_sha256":"8a8d1373a5c54f4ec92185deacfcb9c3169ce67c11949290ee279d8e3a000552"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wj9/3nbbHw8BU1nASJYC+PcMNv15RDRpJMXFRhbVNUGVeYEd8SIOIE4zBQ93SKJ34sJvr/rEtulgL1I9OPODBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:42:37.045721Z","bundle_sha256":"d210c92d80d1bbf0ae43fffef9bea4407480657ef7e48c0ed01267a6ff264d70"}}