{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:75YOTOGYPNCKMWEDTG544BTLTA","short_pith_number":"pith:75YOTOGY","canonical_record":{"source":{"id":"2607.13279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-14T21:30:39Z","cross_cats_sorted":["math.OC","math.SP"],"title_canon_sha256":"f731d56d1f0f0468695915a508a8bac73533c69d41c38f234fa92534fd525ed7","abstract_canon_sha256":"f290f9dc39e1037a7d35c9c861546ffa6087263c9aacee87b7031bd57a066fc7"},"schema_version":"1.0"},"canonical_sha256":"ff70e9b8d87b44a6588399bbce066b9809baf1673d91524351f3ceff08a103e9","source":{"kind":"arxiv","id":"2607.13279","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13279","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13279v1","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13279","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"75YOTOGYPNCK","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"pith_short_16","alias_value":"75YOTOGYPNCKMWED","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"pith_short_8","alias_value":"75YOTOGY","created_at":"2026-07-16T00:22:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:75YOTOGYPNCKMWEDTG544BTLTA","target":"record","payload":{"canonical_record":{"source":{"id":"2607.13279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-14T21:30:39Z","cross_cats_sorted":["math.OC","math.SP"],"title_canon_sha256":"f731d56d1f0f0468695915a508a8bac73533c69d41c38f234fa92534fd525ed7","abstract_canon_sha256":"f290f9dc39e1037a7d35c9c861546ffa6087263c9aacee87b7031bd57a066fc7"},"schema_version":"1.0"},"canonical_sha256":"ff70e9b8d87b44a6588399bbce066b9809baf1673d91524351f3ceff08a103e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T00:22:07.344499Z","signature_b64":"jY/8tRTONrs0rdy77Fv5ZiFVDdaEnATS1yRcRcy2FqIdfUd3xNu0wQCUFkhGVcPS0ffHL+wBVERmOme4MtURDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff70e9b8d87b44a6588399bbce066b9809baf1673d91524351f3ceff08a103e9","last_reissued_at":"2026-07-16T00:22:07.343717Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T00:22:07.343717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.13279","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":"2026-07-16T00:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jHxclgpodfyQnTgwfUdpDBk4+i4/41wnWbgw0P0tovZd2VQ8mf2Z7BEmmPLTBX0UZ5yssfWTBVcx4K0edQSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:47:29.674208Z"},"content_sha256":"00fbb40746b29de6b242fc1a0f6cd3320d41b04eaeaf1700aa0e7cc41a53f0db","schema_version":"1.0","event_id":"sha256:00fbb40746b29de6b242fc1a0f6cd3320d41b04eaeaf1700aa0e7cc41a53f0db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:75YOTOGYPNCKMWEDTG544BTLTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.SP"],"primary_cat":"math.AP","authors_text":"Amaury Hayat, Emmanuel Tr\\'elat, Vincent Boulard","submitted_at":"2026-07-14T21:30:39Z","abstract_excerpt":"Weighted integrated observability inequalities for heat equations usually involve a small-time factor of the form $e^{-\\gamma/t}$. We prove that this scale is not an artefact of Carleman or spectral methods: it is forced by the geometry of the observation set.\n  Let $A$ be a nonnegative self-adjoint operator on sections of a finite-rank Euclidean vector bundle over a doubling metric measure space, satisfying ultracontractivity, Davies-Gaffney estimates (equivalently, finite speed of propagation for the wave equation) and a pointwise local Weyl law. If a weighted integrated observability inequa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13279","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13279/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":"2026-07-16T00:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mD1HbOyrt3f+94KIxNMkQewKYrFQj4UZhlFxJ1Xza72/HtWMeMkYbScIP7SOK54Kw8x0KxYJYX8RmHnsuaA5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:47:29.674989Z"},"content_sha256":"8e79b5d2297bd5481c71eb385889074de8a96818cd67b80b5450e284a06525bf","schema_version":"1.0","event_id":"sha256:8e79b5d2297bd5481c71eb385889074de8a96818cd67b80b5450e284a06525bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/75YOTOGYPNCKMWEDTG544BTLTA/bundle.json","state_url":"https://pith.science/pith/75YOTOGYPNCKMWEDTG544BTLTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/75YOTOGYPNCKMWEDTG544BTLTA/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":"2026-08-12T20:47:29Z","links":{"resolver":"https://pith.science/pith/75YOTOGYPNCKMWEDTG544BTLTA","bundle":"https://pith.science/pith/75YOTOGYPNCKMWEDTG544BTLTA/bundle.json","state":"https://pith.science/pith/75YOTOGYPNCKMWEDTG544BTLTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/75YOTOGYPNCKMWEDTG544BTLTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:75YOTOGYPNCKMWEDTG544BTLTA","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":"f290f9dc39e1037a7d35c9c861546ffa6087263c9aacee87b7031bd57a066fc7","cross_cats_sorted":["math.OC","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-14T21:30:39Z","title_canon_sha256":"f731d56d1f0f0468695915a508a8bac73533c69d41c38f234fa92534fd525ed7"},"schema_version":"1.0","source":{"id":"2607.13279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13279","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13279v1","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13279","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"75YOTOGYPNCK","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"pith_short_16","alias_value":"75YOTOGYPNCKMWED","created_at":"2026-07-16T00:22:07Z"},{"alias_kind":"pith_short_8","alias_value":"75YOTOGY","created_at":"2026-07-16T00:22:07Z"}],"graph_snapshots":[{"event_id":"sha256:8e79b5d2297bd5481c71eb385889074de8a96818cd67b80b5450e284a06525bf","target":"graph","created_at":"2026-07-16T00:22:07Z","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/2607.13279/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Weighted integrated observability inequalities for heat equations usually involve a small-time factor of the form $e^{-\\gamma/t}$. We prove that this scale is not an artefact of Carleman or spectral methods: it is forced by the geometry of the observation set.\n  Let $A$ be a nonnegative self-adjoint operator on sections of a finite-rank Euclidean vector bundle over a doubling metric measure space, satisfying ultracontractivity, Davies-Gaffney estimates (equivalently, finite speed of propagation for the wave equation) and a pointwise local Weyl law. If a weighted integrated observability inequa","authors_text":"Amaury Hayat, Emmanuel Tr\\'elat, Vincent Boulard","cross_cats":["math.OC","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-14T21:30:39Z","title":"Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13279","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":"sha256:00fbb40746b29de6b242fc1a0f6cd3320d41b04eaeaf1700aa0e7cc41a53f0db","target":"record","created_at":"2026-07-16T00:22:07Z","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":"f290f9dc39e1037a7d35c9c861546ffa6087263c9aacee87b7031bd57a066fc7","cross_cats_sorted":["math.OC","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-14T21:30:39Z","title_canon_sha256":"f731d56d1f0f0468695915a508a8bac73533c69d41c38f234fa92534fd525ed7"},"schema_version":"1.0","source":{"id":"2607.13279","kind":"arxiv","version":1}},"canonical_sha256":"ff70e9b8d87b44a6588399bbce066b9809baf1673d91524351f3ceff08a103e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff70e9b8d87b44a6588399bbce066b9809baf1673d91524351f3ceff08a103e9","first_computed_at":"2026-07-16T00:22:07.343717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T00:22:07.343717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jY/8tRTONrs0rdy77Fv5ZiFVDdaEnATS1yRcRcy2FqIdfUd3xNu0wQCUFkhGVcPS0ffHL+wBVERmOme4MtURDA==","signature_status":"signed_v1","signed_at":"2026-07-16T00:22:07.344499Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00fbb40746b29de6b242fc1a0f6cd3320d41b04eaeaf1700aa0e7cc41a53f0db","sha256:8e79b5d2297bd5481c71eb385889074de8a96818cd67b80b5450e284a06525bf"],"state_sha256":"dbe8fb38514922881d59138d1b39989660b1135cef1cc1e94c9d18a53ec9e738"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Me/pE3Hb7ifVESocBPhlwqUodsi3G2JBM+fA1dFGGc0/qjM5CfzMfH1Z1RNa+olLjbeBOJBmCGtfAwmpz/SzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T20:47:29.681177Z","bundle_sha256":"df3d656b20df65899f0d5917b9080a9ea5a310038adab7af5bba7870d95f41c3"}}