{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TMVTEXGFMKYKWCVM5IQDIQXXRQ","short_pith_number":"pith:TMVTEXGF","canonical_record":{"source":{"id":"2409.03908","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-05T20:58:23Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"79c7218f9076c37963decb2be933a6e6a1d42e79b0307df61cfdcb18db31c50b","abstract_canon_sha256":"0051368b559e0a2c1062251575cc54b54f6d484a918136e4a33aeb2430bccb07"},"schema_version":"1.0"},"canonical_sha256":"9b2b325cc562b0ab0aacea203442f78c10723d2226c7e0304651ee0ad8cdfe7c","source":{"kind":"arxiv","id":"2409.03908","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.03908","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"2409.03908v3","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.03908","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"TMVTEXGFMKYK","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"pith_short_16","alias_value":"TMVTEXGFMKYKWCVM","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"pith_short_8","alias_value":"TMVTEXGF","created_at":"2026-07-05T11:10:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TMVTEXGFMKYKWCVM5IQDIQXXRQ","target":"record","payload":{"canonical_record":{"source":{"id":"2409.03908","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-05T20:58:23Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"79c7218f9076c37963decb2be933a6e6a1d42e79b0307df61cfdcb18db31c50b","abstract_canon_sha256":"0051368b559e0a2c1062251575cc54b54f6d484a918136e4a33aeb2430bccb07"},"schema_version":"1.0"},"canonical_sha256":"9b2b325cc562b0ab0aacea203442f78c10723d2226c7e0304651ee0ad8cdfe7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:47.334753Z","signature_b64":"8/Ze0AUf4IOb2SdNgW+dgieLYC6HCO8t1DYElg4/jZxN6pbgVa88N23JvkdieqvEpOFOEBj4KViWlbsYTIicCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b2b325cc562b0ab0aacea203442f78c10723d2226c7e0304651ee0ad8cdfe7c","last_reissued_at":"2026-07-05T11:10:47.334013Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:47.334013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.03908","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bKjoT3Cy7cpHn/g57Gs2J0qtCbHqNbwu8P1e2hAk+QBuI0dhuycoHYCn0cCzX4NHSvW4D6lPnNoUy54/qeVgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:10:32.197154Z"},"content_sha256":"769cb1239ac3f0d30f380c63cea9bcc9d2e0d76cdd50510675550e3ead1993e3","schema_version":"1.0","event_id":"sha256:769cb1239ac3f0d30f380c63cea9bcc9d2e0d76cdd50510675550e3ead1993e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TMVTEXGFMKYKWCVM5IQDIQXXRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Lawford Hatcher","submitted_at":"2024-09-05T20:58:23Z","abstract_excerpt":"We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two seemingly new estimates on the first mixed eigenvalue to give explicit examples of when the Dirichlet region is sufficiently small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.03908","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.03908/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3cxJ8e9sthioypbrAt3slKhZS+Z6R0T2dRg3lTeOi2JD2oQY6cmGik3RsjTfBsZE5ZW3R7reqhsohe1c459tBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:10:32.198380Z"},"content_sha256":"10a8181ebcf950399abd01d1bfc7bd3adb41be7ac944cba6c8ad2d91f9da8413","schema_version":"1.0","event_id":"sha256:10a8181ebcf950399abd01d1bfc7bd3adb41be7ac944cba6c8ad2d91f9da8413"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMVTEXGFMKYKWCVM5IQDIQXXRQ/bundle.json","state_url":"https://pith.science/pith/TMVTEXGFMKYKWCVM5IQDIQXXRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMVTEXGFMKYKWCVM5IQDIQXXRQ/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":"2026-08-14T19:10:32Z","links":{"resolver":"https://pith.science/pith/TMVTEXGFMKYKWCVM5IQDIQXXRQ","bundle":"https://pith.science/pith/TMVTEXGFMKYKWCVM5IQDIQXXRQ/bundle.json","state":"https://pith.science/pith/TMVTEXGFMKYKWCVM5IQDIQXXRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMVTEXGFMKYKWCVM5IQDIQXXRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TMVTEXGFMKYKWCVM5IQDIQXXRQ","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":"0051368b559e0a2c1062251575cc54b54f6d484a918136e4a33aeb2430bccb07","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-05T20:58:23Z","title_canon_sha256":"79c7218f9076c37963decb2be933a6e6a1d42e79b0307df61cfdcb18db31c50b"},"schema_version":"1.0","source":{"id":"2409.03908","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.03908","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"2409.03908v3","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.03908","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"TMVTEXGFMKYK","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"pith_short_16","alias_value":"TMVTEXGFMKYKWCVM","created_at":"2026-07-05T11:10:47Z"},{"alias_kind":"pith_short_8","alias_value":"TMVTEXGF","created_at":"2026-07-05T11:10:47Z"}],"graph_snapshots":[{"event_id":"sha256:10a8181ebcf950399abd01d1bfc7bd3adb41be7ac944cba6c8ad2d91f9da8413","target":"graph","created_at":"2026-07-05T11:10:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.03908/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two seemingly new estimates on the first mixed eigenvalue to give explicit examples of when the Dirichlet region is sufficiently small.","authors_text":"Lawford Hatcher","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-05T20:58:23Z","title":"A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.03908","kind":"arxiv","version":3},"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":"sha256:769cb1239ac3f0d30f380c63cea9bcc9d2e0d76cdd50510675550e3ead1993e3","target":"record","created_at":"2026-07-05T11:10:47Z","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":"0051368b559e0a2c1062251575cc54b54f6d484a918136e4a33aeb2430bccb07","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-05T20:58:23Z","title_canon_sha256":"79c7218f9076c37963decb2be933a6e6a1d42e79b0307df61cfdcb18db31c50b"},"schema_version":"1.0","source":{"id":"2409.03908","kind":"arxiv","version":3}},"canonical_sha256":"9b2b325cc562b0ab0aacea203442f78c10723d2226c7e0304651ee0ad8cdfe7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b2b325cc562b0ab0aacea203442f78c10723d2226c7e0304651ee0ad8cdfe7c","first_computed_at":"2026-07-05T11:10:47.334013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:47.334013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8/Ze0AUf4IOb2SdNgW+dgieLYC6HCO8t1DYElg4/jZxN6pbgVa88N23JvkdieqvEpOFOEBj4KViWlbsYTIicCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:47.334753Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.03908","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:769cb1239ac3f0d30f380c63cea9bcc9d2e0d76cdd50510675550e3ead1993e3","sha256:10a8181ebcf950399abd01d1bfc7bd3adb41be7ac944cba6c8ad2d91f9da8413"],"state_sha256":"4cb8e8ebda6dcfcd0a4265570216ff4f1abbd6dc2fc116993c31f22d89e0c787"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gFEHkndwcXuZGv0GD6XTb7i211dO/4G0ElQ/jimIQeMVEd8AluuBibSLQdSgj52ZpyqdNxR+U65QQ29TQ5DKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T19:10:32.203437Z","bundle_sha256":"d077fbd42912782f3ef5ea22e523220767c9b2b1445c7b45fb2f76ee7d8fd808"}}