{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VVOJWWCS6CMJ35UIYN3B4DQZRO","short_pith_number":"pith:VVOJWWCS","canonical_record":{"source":{"id":"1009.2529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-13T21:54:03Z","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"title_canon_sha256":"36e8620ce6646b9039f3c1d714525a358beec560cf2f2018da79288ff3721f67","abstract_canon_sha256":"73e09005761cfde4f4e17e6901a78eae92d41b0a6be8c7429b748465c5aa98db"},"schema_version":"1.0"},"canonical_sha256":"ad5c9b5852f0989df688c3761e0e198ba81ff69f33e91958cd2bfc969fe33192","source":{"kind":"arxiv","id":"1009.2529","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2529","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2529v1","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2529","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"pith_short_12","alias_value":"VVOJWWCS6CMJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VVOJWWCS6CMJ35UI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VVOJWWCS","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VVOJWWCS6CMJ35UIYN3B4DQZRO","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-13T21:54:03Z","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"title_canon_sha256":"36e8620ce6646b9039f3c1d714525a358beec560cf2f2018da79288ff3721f67","abstract_canon_sha256":"73e09005761cfde4f4e17e6901a78eae92d41b0a6be8c7429b748465c5aa98db"},"schema_version":"1.0"},"canonical_sha256":"ad5c9b5852f0989df688c3761e0e198ba81ff69f33e91958cd2bfc969fe33192","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:56.902439Z","signature_b64":"SyDFsXNudzkl5FuGucIftsuUGnFfjU9JqgpcgNM69qYj1WTwGQnerrtbSCYyk3vlRX2xCUOc2f88FpLS8moIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad5c9b5852f0989df688c3761e0e198ba81ff69f33e91958cd2bfc969fe33192","last_reissued_at":"2026-05-18T04:40:56.901829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:56.901829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2529","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":"2026-05-18T04:40:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47S/eTKW23pqAE1gbONSP7TjE5SdbqD94gnWz4W5HJ5NzsX8cCXEEB/p26Ahol3dZdqGHIWwL4vWPbIN2/ybBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:57:57.098727Z"},"content_sha256":"9cd7cefb4ef5f7fc3ef35c7791879d819d25283400c11ad619b41a00300a0d14","schema_version":"1.0","event_id":"sha256:9cd7cefb4ef5f7fc3ef35c7791879d819d25283400c11ad619b41a00300a0d14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VVOJWWCS6CMJ35UIYN3B4DQZRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time-Dependent Attractor for the Oscillon Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Francesco Di Plinio, Gregory S. Duane, Roger Temam","submitted_at":"2010-09-13T21:54:03Z","abstract_excerpt":"We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of arbitrary polynomial growth. After constructing a suitable dynamical framework to deal with the explicit time dependence of the energy of the solution, we establish the existence of a regular, time-dependent global attractor. The sections of the attractor at given times have finite fractal dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2529","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":"2026-05-18T04:40:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UayIKGatParX0NGvvXKB25t2nQ3dDO3HTMGiHWuEA5DIvnAU6rHPFoQOwKd2RMmWxpBjbLVETn1PqOIouzhvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:57:57.099068Z"},"content_sha256":"f2e2cf0a103783c06f3c95506664fea315583123af18643d60afdbbadc52eb37","schema_version":"1.0","event_id":"sha256:f2e2cf0a103783c06f3c95506664fea315583123af18643d60afdbbadc52eb37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVOJWWCS6CMJ35UIYN3B4DQZRO/bundle.json","state_url":"https://pith.science/pith/VVOJWWCS6CMJ35UIYN3B4DQZRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVOJWWCS6CMJ35UIYN3B4DQZRO/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":"2026-06-05T11:57:57Z","links":{"resolver":"https://pith.science/pith/VVOJWWCS6CMJ35UIYN3B4DQZRO","bundle":"https://pith.science/pith/VVOJWWCS6CMJ35UIYN3B4DQZRO/bundle.json","state":"https://pith.science/pith/VVOJWWCS6CMJ35UIYN3B4DQZRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVOJWWCS6CMJ35UIYN3B4DQZRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VVOJWWCS6CMJ35UIYN3B4DQZRO","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":"73e09005761cfde4f4e17e6901a78eae92d41b0a6be8c7429b748465c5aa98db","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-13T21:54:03Z","title_canon_sha256":"36e8620ce6646b9039f3c1d714525a358beec560cf2f2018da79288ff3721f67"},"schema_version":"1.0","source":{"id":"1009.2529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2529","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2529v1","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2529","created_at":"2026-05-18T04:40:56Z"},{"alias_kind":"pith_short_12","alias_value":"VVOJWWCS6CMJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VVOJWWCS6CMJ35UI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VVOJWWCS","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:f2e2cf0a103783c06f3c95506664fea315583123af18643d60afdbbadc52eb37","target":"graph","created_at":"2026-05-18T04:40:56Z","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 investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of arbitrary polynomial growth. After constructing a suitable dynamical framework to deal with the explicit time dependence of the energy of the solution, we establish the existence of a regular, time-dependent global attractor. The sections of the attractor at given times have finite fractal dimension.","authors_text":"Francesco Di Plinio, Gregory S. Duane, Roger Temam","cross_cats":["gr-qc","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-13T21:54:03Z","title":"Time-Dependent Attractor for the Oscillon Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2529","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":"sha256:9cd7cefb4ef5f7fc3ef35c7791879d819d25283400c11ad619b41a00300a0d14","target":"record","created_at":"2026-05-18T04:40:56Z","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":"73e09005761cfde4f4e17e6901a78eae92d41b0a6be8c7429b748465c5aa98db","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-09-13T21:54:03Z","title_canon_sha256":"36e8620ce6646b9039f3c1d714525a358beec560cf2f2018da79288ff3721f67"},"schema_version":"1.0","source":{"id":"1009.2529","kind":"arxiv","version":1}},"canonical_sha256":"ad5c9b5852f0989df688c3761e0e198ba81ff69f33e91958cd2bfc969fe33192","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad5c9b5852f0989df688c3761e0e198ba81ff69f33e91958cd2bfc969fe33192","first_computed_at":"2026-05-18T04:40:56.901829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:56.901829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SyDFsXNudzkl5FuGucIftsuUGnFfjU9JqgpcgNM69qYj1WTwGQnerrtbSCYyk3vlRX2xCUOc2f88FpLS8moIDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:56.902439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cd7cefb4ef5f7fc3ef35c7791879d819d25283400c11ad619b41a00300a0d14","sha256:f2e2cf0a103783c06f3c95506664fea315583123af18643d60afdbbadc52eb37"],"state_sha256":"bbea69710f712a75aace84323063cccd5d8f6bfccc1aa92e0066cc000083c7b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RMHwdWQNXhH0Pyye9PiQTxyGFeKRjOJoK8Ib3PGWfHUW3iWP1kKtBzngNCAteEqXtAstreZIYJ6Z+Oh0/ISeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:57:57.101071Z","bundle_sha256":"922aaac7f8fe9b616d4def06b361885770161507c8d3add85c665ab2014dc76d"}}