{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VCEZLIJ5YZESCP5SIQ7WXEV7E5","short_pith_number":"pith:VCEZLIJ5","canonical_record":{"source":{"id":"0909.2093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-11T06:36:34Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"bc30d62760384082fa895e6802178df12653523a86c062b405522e482703b5af","abstract_canon_sha256":"c34160dce670f095c28911ea8bd19bfd6df1ca3f138fe8e024c4e59eec250e88"},"schema_version":"1.0"},"canonical_sha256":"a88995a13dc649213fb2443f6b92bf2744ffda2345c0ec7bb0c3a24b75ed33e8","source":{"kind":"arxiv","id":"0909.2093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2093","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2093v1","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2093","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"VCEZLIJ5YZES","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VCEZLIJ5YZESCP5S","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VCEZLIJ5","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VCEZLIJ5YZESCP5SIQ7WXEV7E5","target":"record","payload":{"canonical_record":{"source":{"id":"0909.2093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-11T06:36:34Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"bc30d62760384082fa895e6802178df12653523a86c062b405522e482703b5af","abstract_canon_sha256":"c34160dce670f095c28911ea8bd19bfd6df1ca3f138fe8e024c4e59eec250e88"},"schema_version":"1.0"},"canonical_sha256":"a88995a13dc649213fb2443f6b92bf2744ffda2345c0ec7bb0c3a24b75ed33e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:57.163651Z","signature_b64":"7jaFN0tq/kRm01s8KL8NZ8zw/tn2XLaZy/BSAecZGIPQNMAe6Pnb2H+CeXuNWjOwpzdVNf86RzQkHCa0C0GyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a88995a13dc649213fb2443f6b92bf2744ffda2345c0ec7bb0c3a24b75ed33e8","last_reissued_at":"2026-05-18T02:11:57.162835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:57.162835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.2093","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":"2026-05-18T02:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HdII5a1UgJ7+eOqtSk3Ewow0+F6jT8J44W+nB6cNN0zd1Qt928OZyhzD0HmVx4g2RJz1lBgK1TgQTlT9IWVvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:02:15.556296Z"},"content_sha256":"6b87134e8a9ed0bc68e5fbde9777a2d16bc0175ddf6fd15a8a6b5bf27bf9cefe","schema_version":"1.0","event_id":"sha256:6b87134e8a9ed0bc68e5fbde9777a2d16bc0175ddf6fd15a8a6b5bf27bf9cefe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VCEZLIJ5YZESCP5SIQ7WXEV7E5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy decay for the damped wave equation under a pressure condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Emmanuel Schenck (IPHT)","submitted_at":"2009-09-11T06:36:34Z","abstract_excerpt":"We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by the imaginary part of a finite number of eigenvalues close to the real axis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2093","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":"2026-05-18T02:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8VtCDLceGQ0ttNzzzDvfFWhtgheSCOXXT6/KkM2z5x+cv21R24pVM+2Kqy4UZpSyXepfEi4I7ZaLK+uJT+VoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:02:15.556717Z"},"content_sha256":"c93337a55d878b96145e7cd4f67f4c68bcfa2560e2904821e927fb4ce86c22d0","schema_version":"1.0","event_id":"sha256:c93337a55d878b96145e7cd4f67f4c68bcfa2560e2904821e927fb4ce86c22d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCEZLIJ5YZESCP5SIQ7WXEV7E5/bundle.json","state_url":"https://pith.science/pith/VCEZLIJ5YZESCP5SIQ7WXEV7E5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCEZLIJ5YZESCP5SIQ7WXEV7E5/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":"2026-06-07T07:02:15Z","links":{"resolver":"https://pith.science/pith/VCEZLIJ5YZESCP5SIQ7WXEV7E5","bundle":"https://pith.science/pith/VCEZLIJ5YZESCP5SIQ7WXEV7E5/bundle.json","state":"https://pith.science/pith/VCEZLIJ5YZESCP5SIQ7WXEV7E5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCEZLIJ5YZESCP5SIQ7WXEV7E5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VCEZLIJ5YZESCP5SIQ7WXEV7E5","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":"c34160dce670f095c28911ea8bd19bfd6df1ca3f138fe8e024c4e59eec250e88","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-11T06:36:34Z","title_canon_sha256":"bc30d62760384082fa895e6802178df12653523a86c062b405522e482703b5af"},"schema_version":"1.0","source":{"id":"0909.2093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2093","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2093v1","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2093","created_at":"2026-05-18T02:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"VCEZLIJ5YZES","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VCEZLIJ5YZESCP5S","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VCEZLIJ5","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:c93337a55d878b96145e7cd4f67f4c68bcfa2560e2904821e927fb4ce86c22d0","target":"graph","created_at":"2026-05-18T02:11:57Z","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 establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by the imaginary part of a finite number of eigenvalues close to the real axis.","authors_text":"Emmanuel Schenck (IPHT)","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-11T06:36:34Z","title":"Energy decay for the damped wave equation under a pressure condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2093","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":"sha256:6b87134e8a9ed0bc68e5fbde9777a2d16bc0175ddf6fd15a8a6b5bf27bf9cefe","target":"record","created_at":"2026-05-18T02:11:57Z","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":"c34160dce670f095c28911ea8bd19bfd6df1ca3f138fe8e024c4e59eec250e88","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-09-11T06:36:34Z","title_canon_sha256":"bc30d62760384082fa895e6802178df12653523a86c062b405522e482703b5af"},"schema_version":"1.0","source":{"id":"0909.2093","kind":"arxiv","version":1}},"canonical_sha256":"a88995a13dc649213fb2443f6b92bf2744ffda2345c0ec7bb0c3a24b75ed33e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a88995a13dc649213fb2443f6b92bf2744ffda2345c0ec7bb0c3a24b75ed33e8","first_computed_at":"2026-05-18T02:11:57.162835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:57.162835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7jaFN0tq/kRm01s8KL8NZ8zw/tn2XLaZy/BSAecZGIPQNMAe6Pnb2H+CeXuNWjOwpzdVNf86RzQkHCa0C0GyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:57.163651Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.2093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b87134e8a9ed0bc68e5fbde9777a2d16bc0175ddf6fd15a8a6b5bf27bf9cefe","sha256:c93337a55d878b96145e7cd4f67f4c68bcfa2560e2904821e927fb4ce86c22d0"],"state_sha256":"867aa5425c2503d709cb65da2b4a6f907bd2d139f93b3dec7457fb151b910ad4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKfctWDIYSIx9wQi0ewrpzAOEcWznkP99PIVVhH+wH6gXm3WOUHhHcun/R/k1Ldp+C/bUj6jLdbx7YyZvDPsAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:02:15.558996Z","bundle_sha256":"3e409b1c810110ce4dac336af9243eed20f14f3d6555e6ddea56003131815e8d"}}