{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZSJHWR3LCVES27NMVUFYRBWZYX","short_pith_number":"pith:ZSJHWR3L","canonical_record":{"source":{"id":"1709.04197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-13T09:05:29Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"eabe43366e0e40aa744a0c3a24233d9783cb2631fb2f0213d0afeb7d4a75d240","abstract_canon_sha256":"30c981882877e62e3049b8f57c3bc0bd7114aa97e86cf465f95f8837b7a0559f"},"schema_version":"1.0"},"canonical_sha256":"cc927b476b15492d7dacad0b8886d9c5da0f49572bd6e88da004b25b4643022b","source":{"kind":"arxiv","id":"1709.04197","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04197","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04197v1","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04197","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZSJHWR3LCVES","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZSJHWR3LCVES27NM","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZSJHWR3L","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZSJHWR3LCVES27NMVUFYRBWZYX","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-13T09:05:29Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"eabe43366e0e40aa744a0c3a24233d9783cb2631fb2f0213d0afeb7d4a75d240","abstract_canon_sha256":"30c981882877e62e3049b8f57c3bc0bd7114aa97e86cf465f95f8837b7a0559f"},"schema_version":"1.0"},"canonical_sha256":"cc927b476b15492d7dacad0b8886d9c5da0f49572bd6e88da004b25b4643022b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:15.133101Z","signature_b64":"/P+6ionHEqHx8f5Z+AAcWjj1KauxMk0bPlr8sLM1oRftSA/UV91cYgKicOXBos1XMD4abwkPZcuCSH1BaKYkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc927b476b15492d7dacad0b8886d9c5da0f49572bd6e88da004b25b4643022b","last_reissued_at":"2026-05-18T00:35:15.132544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:15.132544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04197","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":"2026-05-18T00:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CdIGw9qHgNtdgr15F7jX71n8NKHsxQqcWK7piw3icAq92z5CxEIeCT90PA/JApjFWZsNLOA7tmxXzv5hviwVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:08:41.204215Z"},"content_sha256":"cbb2599444da0f2ab4ec00c62206c8fde88f6df42b855a16a1a5b38a48aeeebf","schema_version":"1.0","event_id":"sha256:cbb2599444da0f2ab4ec00c62206c8fde88f6df42b855a16a1a5b38a48aeeebf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZSJHWR3LCVES27NMVUFYRBWZYX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy decay for the Klein-Gordon equation with highly oscillating damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Julien Royer (IMT)","submitted_at":"2017-09-13T09:05:29Z","abstract_excerpt":"We consider the free Klein-Gordon equation with periodic damping. We show on this simple model that if the usual geometric condition holds then the decay of the energy is uniform with respect to the oscillations of the damping, and in particular the size of the derivatives do not play any role. We also show that without geometric condition the polynomial decay of the energy is even slightly better for a highly oscillating damping. To prove these estimates we provide a parameter dependent version of well known results of semigroup theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04197","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":"2026-05-18T00:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D8VAjxv8CEzj7lwXvll+MBczwDYCsoiVOBBwDyuUTOD1qF1td+e79pFCQNQq1kA4Sh6dMMpqQ0ZuQnoB7p4ZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:08:41.204597Z"},"content_sha256":"3ce386f3597facb68a33f02d83f6061e0fffef827fbb6be92675555a4f16eb8b","schema_version":"1.0","event_id":"sha256:3ce386f3597facb68a33f02d83f6061e0fffef827fbb6be92675555a4f16eb8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZSJHWR3LCVES27NMVUFYRBWZYX/bundle.json","state_url":"https://pith.science/pith/ZSJHWR3LCVES27NMVUFYRBWZYX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZSJHWR3LCVES27NMVUFYRBWZYX/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":"2026-05-28T10:08:41Z","links":{"resolver":"https://pith.science/pith/ZSJHWR3LCVES27NMVUFYRBWZYX","bundle":"https://pith.science/pith/ZSJHWR3LCVES27NMVUFYRBWZYX/bundle.json","state":"https://pith.science/pith/ZSJHWR3LCVES27NMVUFYRBWZYX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZSJHWR3LCVES27NMVUFYRBWZYX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZSJHWR3LCVES27NMVUFYRBWZYX","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":"30c981882877e62e3049b8f57c3bc0bd7114aa97e86cf465f95f8837b7a0559f","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-13T09:05:29Z","title_canon_sha256":"eabe43366e0e40aa744a0c3a24233d9783cb2631fb2f0213d0afeb7d4a75d240"},"schema_version":"1.0","source":{"id":"1709.04197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04197","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04197v1","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04197","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZSJHWR3LCVES","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZSJHWR3LCVES27NM","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZSJHWR3L","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:3ce386f3597facb68a33f02d83f6061e0fffef827fbb6be92675555a4f16eb8b","target":"graph","created_at":"2026-05-18T00:35:15Z","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 consider the free Klein-Gordon equation with periodic damping. We show on this simple model that if the usual geometric condition holds then the decay of the energy is uniform with respect to the oscillations of the damping, and in particular the size of the derivatives do not play any role. We also show that without geometric condition the polynomial decay of the energy is even slightly better for a highly oscillating damping. To prove these estimates we provide a parameter dependent version of well known results of semigroup theory.","authors_text":"Julien Royer (IMT)","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-13T09:05:29Z","title":"Energy decay for the Klein-Gordon equation with highly oscillating damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04197","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:cbb2599444da0f2ab4ec00c62206c8fde88f6df42b855a16a1a5b38a48aeeebf","target":"record","created_at":"2026-05-18T00:35:15Z","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":"30c981882877e62e3049b8f57c3bc0bd7114aa97e86cf465f95f8837b7a0559f","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-13T09:05:29Z","title_canon_sha256":"eabe43366e0e40aa744a0c3a24233d9783cb2631fb2f0213d0afeb7d4a75d240"},"schema_version":"1.0","source":{"id":"1709.04197","kind":"arxiv","version":1}},"canonical_sha256":"cc927b476b15492d7dacad0b8886d9c5da0f49572bd6e88da004b25b4643022b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc927b476b15492d7dacad0b8886d9c5da0f49572bd6e88da004b25b4643022b","first_computed_at":"2026-05-18T00:35:15.132544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:15.132544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/P+6ionHEqHx8f5Z+AAcWjj1KauxMk0bPlr8sLM1oRftSA/UV91cYgKicOXBos1XMD4abwkPZcuCSH1BaKYkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:15.133101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbb2599444da0f2ab4ec00c62206c8fde88f6df42b855a16a1a5b38a48aeeebf","sha256:3ce386f3597facb68a33f02d83f6061e0fffef827fbb6be92675555a4f16eb8b"],"state_sha256":"f17e22d1ac0f05e4952f40e9d1d1c94d599fae2abf3ee55e48707d0c535463ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fmuEhDRjS+9TdvlGsoTKXzDTFMN4zOPlXe34dHGnTfZ2ioFQ1C//aUnQ2MZW9ZP6nsN0/piq/QbpvMAfE07zBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:08:41.206532Z","bundle_sha256":"f429abebef101abd72cf8ad8751089059620d748c64b33541a5a6d020f427f8c"}}