{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SPCZ23RNLFIDU6HPXRTZSXOQCU","short_pith_number":"pith:SPCZ23RN","canonical_record":{"source":{"id":"1206.1381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-07T01:22:44Z","cross_cats_sorted":[],"title_canon_sha256":"a2dd5d356bdc90375b51fcd088c1e27ca02d288a8efb6cc233ecfcacdf2eaba1","abstract_canon_sha256":"b57e995055a133e4704e747bd5b04bf1762c958b64e892f7f08ec4cc46a38b4e"},"schema_version":"1.0"},"canonical_sha256":"93c59d6e2d59503a78efbc67995dd01517e5f14e87f799bafc97a12023c509be","source":{"kind":"arxiv","id":"1206.1381","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1381","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1381v2","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1381","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"pith_short_12","alias_value":"SPCZ23RNLFID","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SPCZ23RNLFIDU6HP","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SPCZ23RN","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SPCZ23RNLFIDU6HPXRTZSXOQCU","target":"record","payload":{"canonical_record":{"source":{"id":"1206.1381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-07T01:22:44Z","cross_cats_sorted":[],"title_canon_sha256":"a2dd5d356bdc90375b51fcd088c1e27ca02d288a8efb6cc233ecfcacdf2eaba1","abstract_canon_sha256":"b57e995055a133e4704e747bd5b04bf1762c958b64e892f7f08ec4cc46a38b4e"},"schema_version":"1.0"},"canonical_sha256":"93c59d6e2d59503a78efbc67995dd01517e5f14e87f799bafc97a12023c509be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:31.808516Z","signature_b64":"6U/Un9xVS4cmodmBHDOQyhxA5ezSqVI70008UZM9fTTb+Cr3r0YpruExqGTIGeetkjSqJKndPEXxCH6SxFEjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93c59d6e2d59503a78efbc67995dd01517e5f14e87f799bafc97a12023c509be","last_reissued_at":"2026-05-18T03:21:31.807994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:31.807994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.1381","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":"2026-05-18T03:21:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZ91lBCIi/YUmUTNEvj7/8Ax/6LMiYKSzw3Dv+HVTfH7AQfGAuwxfZv6VgQeOEAKw01/v6zEXr6WUpwrScQhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:13:32.708586Z"},"content_sha256":"628f21c1e13c418f48ea2b63bc8b766525840af480d8fa30789b1b778f239ff8","schema_version":"1.0","event_id":"sha256:628f21c1e13c418f48ea2b63bc8b766525840af480d8fa30789b1b778f239ff8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SPCZ23RNLFIDU6HPXRTZSXOQCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact spectrum of the Laplacian on a domain in the Sierpinski gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hua Qiu","submitted_at":"2012-06-07T01:22:44Z","abstract_excerpt":"For a certain domain $\\Omega$ in the Sierpinski gasket $\\mathcal{SG}$ whose boundary is a line segment, a complete description of the eigenvalues of the Laplacian, with an exact count of dimensions of eigenspaces, under the Dirichlet and Neumann boundary conditions is presented. The method developed in this paper is a weak version of the spectral decimation method due to Fukushima and Shima, since for a lot of \"bad\" eigenvalues the spectral decimation method can not be used directly. Let $\\rho^0(x)$, $\\rho^\\Omega(x)$ be the eigenvalue counting functions of the Laplacian associated to $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1381","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":"2026-05-18T03:21:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3qkTKycoUfJPB/EmxyQbkFBKYh0YmeZkbL774fSmwTfmYV823esZg0Go86B5qeCMRdL0v3rbVs8U8Ic9EWjqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:13:32.709245Z"},"content_sha256":"2a3ddb4a294b2281332e9478159e71d2eef203413132adb6ed6423a759431c3d","schema_version":"1.0","event_id":"sha256:2a3ddb4a294b2281332e9478159e71d2eef203413132adb6ed6423a759431c3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPCZ23RNLFIDU6HPXRTZSXOQCU/bundle.json","state_url":"https://pith.science/pith/SPCZ23RNLFIDU6HPXRTZSXOQCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPCZ23RNLFIDU6HPXRTZSXOQCU/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":"2026-05-31T04:13:32Z","links":{"resolver":"https://pith.science/pith/SPCZ23RNLFIDU6HPXRTZSXOQCU","bundle":"https://pith.science/pith/SPCZ23RNLFIDU6HPXRTZSXOQCU/bundle.json","state":"https://pith.science/pith/SPCZ23RNLFIDU6HPXRTZSXOQCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPCZ23RNLFIDU6HPXRTZSXOQCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SPCZ23RNLFIDU6HPXRTZSXOQCU","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":"b57e995055a133e4704e747bd5b04bf1762c958b64e892f7f08ec4cc46a38b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-07T01:22:44Z","title_canon_sha256":"a2dd5d356bdc90375b51fcd088c1e27ca02d288a8efb6cc233ecfcacdf2eaba1"},"schema_version":"1.0","source":{"id":"1206.1381","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1381","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1381v2","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1381","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"pith_short_12","alias_value":"SPCZ23RNLFID","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SPCZ23RNLFIDU6HP","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SPCZ23RN","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:2a3ddb4a294b2281332e9478159e71d2eef203413132adb6ed6423a759431c3d","target":"graph","created_at":"2026-05-18T03:21:31Z","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":"For a certain domain $\\Omega$ in the Sierpinski gasket $\\mathcal{SG}$ whose boundary is a line segment, a complete description of the eigenvalues of the Laplacian, with an exact count of dimensions of eigenspaces, under the Dirichlet and Neumann boundary conditions is presented. The method developed in this paper is a weak version of the spectral decimation method due to Fukushima and Shima, since for a lot of \"bad\" eigenvalues the spectral decimation method can not be used directly. Let $\\rho^0(x)$, $\\rho^\\Omega(x)$ be the eigenvalue counting functions of the Laplacian associated to $\\mathcal","authors_text":"Hua Qiu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-07T01:22:44Z","title":"Exact spectrum of the Laplacian on a domain in the Sierpinski gasket"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1381","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":"sha256:628f21c1e13c418f48ea2b63bc8b766525840af480d8fa30789b1b778f239ff8","target":"record","created_at":"2026-05-18T03:21:31Z","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":"b57e995055a133e4704e747bd5b04bf1762c958b64e892f7f08ec4cc46a38b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-07T01:22:44Z","title_canon_sha256":"a2dd5d356bdc90375b51fcd088c1e27ca02d288a8efb6cc233ecfcacdf2eaba1"},"schema_version":"1.0","source":{"id":"1206.1381","kind":"arxiv","version":2}},"canonical_sha256":"93c59d6e2d59503a78efbc67995dd01517e5f14e87f799bafc97a12023c509be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93c59d6e2d59503a78efbc67995dd01517e5f14e87f799bafc97a12023c509be","first_computed_at":"2026-05-18T03:21:31.807994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:31.807994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6U/Un9xVS4cmodmBHDOQyhxA5ezSqVI70008UZM9fTTb+Cr3r0YpruExqGTIGeetkjSqJKndPEXxCH6SxFEjBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:31.808516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1381","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:628f21c1e13c418f48ea2b63bc8b766525840af480d8fa30789b1b778f239ff8","sha256:2a3ddb4a294b2281332e9478159e71d2eef203413132adb6ed6423a759431c3d"],"state_sha256":"e40bf0086ff92ce9b382ab258ab7a834f373419dc7d6ada0faa26ab5f3eaf657"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JF2UNH3+Lhedyrtl7OAagMec1uat9S9VsuuEy/9URhOzhYo5JJkrRONA6aSbrGCwvpKbsCZvgRS9AW5TG7gACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:13:32.712875Z","bundle_sha256":"5f7c5c8c0b7a9d26456d76870e0bea98abb55f2ed5afe9fe4ca75f39a3687711"}}