{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q7DTAIILONY26SNZL2C7YT3SRL","short_pith_number":"pith:Q7DTAIIL","canonical_record":{"source":{"id":"1304.4030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-04-15T09:31:35Z","cross_cats_sorted":[],"title_canon_sha256":"6b457c6a87e8a95e8040413446efe41bdaa718bb81752f5d43a3c79c9ca5e097","abstract_canon_sha256":"d2594223bd444da0debb755a7214d8aa1d6b6b8c16d6641136e1025b648abe5f"},"schema_version":"1.0"},"canonical_sha256":"87c730210b7371af49b95e85fc4f728ae43be07304bc16931b6a1b7a0d69145f","source":{"kind":"arxiv","id":"1304.4030","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4030","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4030v2","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4030","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"Q7DTAIILONY2","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q7DTAIILONY26SNZ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q7DTAIIL","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q7DTAIILONY26SNZL2C7YT3SRL","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-04-15T09:31:35Z","cross_cats_sorted":[],"title_canon_sha256":"6b457c6a87e8a95e8040413446efe41bdaa718bb81752f5d43a3c79c9ca5e097","abstract_canon_sha256":"d2594223bd444da0debb755a7214d8aa1d6b6b8c16d6641136e1025b648abe5f"},"schema_version":"1.0"},"canonical_sha256":"87c730210b7371af49b95e85fc4f728ae43be07304bc16931b6a1b7a0d69145f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.865120Z","signature_b64":"QlGi06XWADn+F8ZoYtFkGp2i26nw84is5XiRrOTdGRTNbUan8xWJF3TSNwHhf0ye8Esksgd2hfRR1zwn5iiuAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87c730210b7371af49b95e85fc4f728ae43be07304bc16931b6a1b7a0d69145f","last_reissued_at":"2026-05-18T00:44:29.864626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.864626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4030","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":"2026-05-18T00:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"meb64rw2oV7/IW3R0sRrVVEzyV+B+YZfC8zZmbLC/SRGgMx9j0QoJEawma6YAqNDBU5krZ6kRudH7f2gZpFVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:30:30.243676Z"},"content_sha256":"4db67cf9e8406ca8a03d213f1edcf5c177e6374e9e3c44c7bd76c4a05d6d7252","schema_version":"1.0","event_id":"sha256:4db67cf9e8406ca8a03d213f1edcf5c177e6374e9e3c44c7bd76c4a05d6d7252"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q7DTAIILONY26SNZL2C7YT3SRL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isospectrality and heat content","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"E. B. Dryden, M. van den Berg, T. Kappeler","submitted_at":"2013-04-15T09:31:35Z","abstract_excerpt":"We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schr\\\"{o}dinger operators acting in $L^2[0,1]$ with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4030","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":"2026-05-18T00:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gGNODsmEZX1hYHpR5bve/BCq85wucsI9HrJYPH9hZvTbZx47SrTOg83qOESyLI4+3YOpevBX4a1ZOXhG9WaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:30:30.244184Z"},"content_sha256":"84a9c57ff2ef54c648c6a68c4f3c1092b74ea6e192467b9d23f3f52d1dd987f8","schema_version":"1.0","event_id":"sha256:84a9c57ff2ef54c648c6a68c4f3c1092b74ea6e192467b9d23f3f52d1dd987f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7DTAIILONY26SNZL2C7YT3SRL/bundle.json","state_url":"https://pith.science/pith/Q7DTAIILONY26SNZL2C7YT3SRL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7DTAIILONY26SNZL2C7YT3SRL/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":"2026-05-27T00:30:30Z","links":{"resolver":"https://pith.science/pith/Q7DTAIILONY26SNZL2C7YT3SRL","bundle":"https://pith.science/pith/Q7DTAIILONY26SNZL2C7YT3SRL/bundle.json","state":"https://pith.science/pith/Q7DTAIILONY26SNZL2C7YT3SRL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7DTAIILONY26SNZL2C7YT3SRL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q7DTAIILONY26SNZL2C7YT3SRL","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":"d2594223bd444da0debb755a7214d8aa1d6b6b8c16d6641136e1025b648abe5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-04-15T09:31:35Z","title_canon_sha256":"6b457c6a87e8a95e8040413446efe41bdaa718bb81752f5d43a3c79c9ca5e097"},"schema_version":"1.0","source":{"id":"1304.4030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4030","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4030v2","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4030","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"Q7DTAIILONY2","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q7DTAIILONY26SNZ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q7DTAIIL","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:84a9c57ff2ef54c648c6a68c4f3c1092b74ea6e192467b9d23f3f52d1dd987f8","target":"graph","created_at":"2026-05-18T00:44:29Z","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 present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schr\\\"{o}dinger operators acting in $L^2[0,1]$ with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.","authors_text":"E. B. Dryden, M. van den Berg, T. Kappeler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-04-15T09:31:35Z","title":"Isospectrality and heat content"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4030","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":"sha256:4db67cf9e8406ca8a03d213f1edcf5c177e6374e9e3c44c7bd76c4a05d6d7252","target":"record","created_at":"2026-05-18T00:44:29Z","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":"d2594223bd444da0debb755a7214d8aa1d6b6b8c16d6641136e1025b648abe5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-04-15T09:31:35Z","title_canon_sha256":"6b457c6a87e8a95e8040413446efe41bdaa718bb81752f5d43a3c79c9ca5e097"},"schema_version":"1.0","source":{"id":"1304.4030","kind":"arxiv","version":2}},"canonical_sha256":"87c730210b7371af49b95e85fc4f728ae43be07304bc16931b6a1b7a0d69145f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87c730210b7371af49b95e85fc4f728ae43be07304bc16931b6a1b7a0d69145f","first_computed_at":"2026-05-18T00:44:29.864626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:29.864626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QlGi06XWADn+F8ZoYtFkGp2i26nw84is5XiRrOTdGRTNbUan8xWJF3TSNwHhf0ye8Esksgd2hfRR1zwn5iiuAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:29.865120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4db67cf9e8406ca8a03d213f1edcf5c177e6374e9e3c44c7bd76c4a05d6d7252","sha256:84a9c57ff2ef54c648c6a68c4f3c1092b74ea6e192467b9d23f3f52d1dd987f8"],"state_sha256":"20192436d821032f9738b81e6c33de76080692b382a032e564347b4b9478fed4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"puYxC/abuG7l7qvwZY7rVm7rhnBu+6YMDsH/klnmNYkRkHVDmXNhJcNyO5LYhmaM5jCxWZY486WyhMukYlGXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:30:30.246862Z","bundle_sha256":"cee5dc03a103080bdf49d7c92c886bb2f66fdb59e1d6f146aa20ea00ed82133e"}}