{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XKC6BMPB2SQUJWMKIYPZKLTJPE","short_pith_number":"pith:XKC6BMPB","canonical_record":{"source":{"id":"1211.0731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-04T23:16:34Z","cross_cats_sorted":[],"title_canon_sha256":"69f066274e6351b7fd2836e0fdb0bf2588e7f9a1a1c57aac131bf2671a60038d","abstract_canon_sha256":"c5dd21d13d883c2aecff08fc315ad8dd55a0027d8727afd9ab78321d6de22c32"},"schema_version":"1.0"},"canonical_sha256":"ba85e0b1e1d4a144d98a461f952e69790fc20454aea934716ce4820a5e22054b","source":{"kind":"arxiv","id":"1211.0731","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0731","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0731v2","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0731","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"XKC6BMPB2SQU","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XKC6BMPB2SQUJWMK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XKC6BMPB","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XKC6BMPB2SQUJWMKIYPZKLTJPE","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-04T23:16:34Z","cross_cats_sorted":[],"title_canon_sha256":"69f066274e6351b7fd2836e0fdb0bf2588e7f9a1a1c57aac131bf2671a60038d","abstract_canon_sha256":"c5dd21d13d883c2aecff08fc315ad8dd55a0027d8727afd9ab78321d6de22c32"},"schema_version":"1.0"},"canonical_sha256":"ba85e0b1e1d4a144d98a461f952e69790fc20454aea934716ce4820a5e22054b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:40.624036Z","signature_b64":"HNVB9wFlJR4RKpljmNERBdfxlHoeNP/xgtD8IAiqpNJIy3TO2XZzisbhrTcHzIVyk+f/8eJz0duMiad19b+UAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba85e0b1e1d4a144d98a461f952e69790fc20454aea934716ce4820a5e22054b","last_reissued_at":"2026-05-18T01:33:40.623527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:40.623527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0731","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":"2026-05-18T01:33:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5tm1LaXBAfDQmbnNV5O+bfE0GxoJlOcbJbu8R9ZCwynNC/ahCBMBOjaLsDdwarKz8BRPDT1obN4pf84GFuIsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:28:00.514086Z"},"content_sha256":"4c60a45383f78d9fc38a1f441a9003451ea49990095f2e2480540063785a42e7","schema_version":"1.0","event_id":"sha256:4c60a45383f78d9fc38a1f441a9003451ea49990095f2e2480540063785a42e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XKC6BMPB2SQUJWMKIYPZKLTJPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Threshold between Effective and Noneffective Damping for Semilinear Waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marcello D'Abbicco","submitted_at":"2012-11-04T23:16:34Z","abstract_excerpt":"In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the linear problem. We extend our results to a model with polynomial speed of propagation and to a model with an exponential speed of propagation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0731","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":"2026-05-18T01:33:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kzEINE8YTiT5sCrE2j5FWpBdZKw9XqXp8nanPKAVbn3sBB1cduQAro4Xm9Div0li76iReEtKcbJiRtTVKfWpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:28:00.514472Z"},"content_sha256":"834d4b82351df7b51aacab15d282de9684881a8346527377a9af28ef5b83a163","schema_version":"1.0","event_id":"sha256:834d4b82351df7b51aacab15d282de9684881a8346527377a9af28ef5b83a163"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XKC6BMPB2SQUJWMKIYPZKLTJPE/bundle.json","state_url":"https://pith.science/pith/XKC6BMPB2SQUJWMKIYPZKLTJPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XKC6BMPB2SQUJWMKIYPZKLTJPE/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":"2026-05-31T02:28:00Z","links":{"resolver":"https://pith.science/pith/XKC6BMPB2SQUJWMKIYPZKLTJPE","bundle":"https://pith.science/pith/XKC6BMPB2SQUJWMKIYPZKLTJPE/bundle.json","state":"https://pith.science/pith/XKC6BMPB2SQUJWMKIYPZKLTJPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XKC6BMPB2SQUJWMKIYPZKLTJPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XKC6BMPB2SQUJWMKIYPZKLTJPE","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":"c5dd21d13d883c2aecff08fc315ad8dd55a0027d8727afd9ab78321d6de22c32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-04T23:16:34Z","title_canon_sha256":"69f066274e6351b7fd2836e0fdb0bf2588e7f9a1a1c57aac131bf2671a60038d"},"schema_version":"1.0","source":{"id":"1211.0731","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0731","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0731v2","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0731","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"XKC6BMPB2SQU","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XKC6BMPB2SQUJWMK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XKC6BMPB","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:834d4b82351df7b51aacab15d282de9684881a8346527377a9af28ef5b83a163","target":"graph","created_at":"2026-05-18T01:33:40Z","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":"In this paper we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with scale-invariant damping. We obtain estimates for the solution and its energy with the same decay rate of the linear problem. We extend our results to a model with polynomial speed of propagation and to a model with an exponential speed of propagation.","authors_text":"Marcello D'Abbicco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-04T23:16:34Z","title":"The Threshold between Effective and Noneffective Damping for Semilinear Waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0731","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":"sha256:4c60a45383f78d9fc38a1f441a9003451ea49990095f2e2480540063785a42e7","target":"record","created_at":"2026-05-18T01:33:40Z","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":"c5dd21d13d883c2aecff08fc315ad8dd55a0027d8727afd9ab78321d6de22c32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-04T23:16:34Z","title_canon_sha256":"69f066274e6351b7fd2836e0fdb0bf2588e7f9a1a1c57aac131bf2671a60038d"},"schema_version":"1.0","source":{"id":"1211.0731","kind":"arxiv","version":2}},"canonical_sha256":"ba85e0b1e1d4a144d98a461f952e69790fc20454aea934716ce4820a5e22054b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba85e0b1e1d4a144d98a461f952e69790fc20454aea934716ce4820a5e22054b","first_computed_at":"2026-05-18T01:33:40.623527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:40.623527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HNVB9wFlJR4RKpljmNERBdfxlHoeNP/xgtD8IAiqpNJIy3TO2XZzisbhrTcHzIVyk+f/8eJz0duMiad19b+UAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:40.624036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0731","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c60a45383f78d9fc38a1f441a9003451ea49990095f2e2480540063785a42e7","sha256:834d4b82351df7b51aacab15d282de9684881a8346527377a9af28ef5b83a163"],"state_sha256":"842d3b9bdfab3735f9300d466fc819253ddf75aa06239098ef8126aaad04e496"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fq2WC61edrnN+Vdb+pIuATXalSuElZIbYqTqhT/+Kn6jyRFG8iMwJ4Fkco5ypk1oB5VqnToEdLd+UOBaoZItCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:28:00.516971Z","bundle_sha256":"bdaff8fd2ca0997626d4847950c04c6f67fe0fd9830f0c05fcea1477480ea308"}}