{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XSHLMB5K46QG6FQMPXZ5KXTGTT","short_pith_number":"pith:XSHLMB5K","canonical_record":{"source":{"id":"1411.6141","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-22T16:52:02Z","cross_cats_sorted":[],"title_canon_sha256":"491c0bb15656ad87f3e134cf10c5e2a78957f9478876617d168b563a4cdad43d","abstract_canon_sha256":"ba0d095bb1534d98b2ff7815097ac0e0f709ee57d8c3913f2a0e30dc71e3a77d"},"schema_version":"1.0"},"canonical_sha256":"bc8eb607aae7a06f160c7df3d55e669ce65dc248b830fea8005a116447f2f9b2","source":{"kind":"arxiv","id":"1411.6141","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6141","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6141v4","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6141","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"XSHLMB5K46QG","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XSHLMB5K46QG6FQM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XSHLMB5K","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XSHLMB5K46QG6FQMPXZ5KXTGTT","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6141","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-22T16:52:02Z","cross_cats_sorted":[],"title_canon_sha256":"491c0bb15656ad87f3e134cf10c5e2a78957f9478876617d168b563a4cdad43d","abstract_canon_sha256":"ba0d095bb1534d98b2ff7815097ac0e0f709ee57d8c3913f2a0e30dc71e3a77d"},"schema_version":"1.0"},"canonical_sha256":"bc8eb607aae7a06f160c7df3d55e669ce65dc248b830fea8005a116447f2f9b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:58.973238Z","signature_b64":"xXVAAdZ6Kei6AxjGBBUmKxcgy3N0cGKo1OutNvfOckSG+yyAVmZW7n2xN5dBSCP7mWDtoauGcNFurHe863wOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc8eb607aae7a06f160c7df3d55e669ce65dc248b830fea8005a116447f2f9b2","last_reissued_at":"2026-05-18T01:15:58.972565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:58.972565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6141","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CB2ST2SpA0wEfFBbmwdXbBts+mZ4G3j/+cJ/8SQqzBMEFJI2+pHzmNDDQJNcy8qTx0XpYavxkIllkrrr7NZNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:40:39.599114Z"},"content_sha256":"1e3598cc59cc6bbc42c8e860fc2a1be2cba7d7182cf58de019fd7400d223340f","schema_version":"1.0","event_id":"sha256:1e3598cc59cc6bbc42c8e860fc2a1be2cba7d7182cf58de019fd7400d223340f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XSHLMB5K46QG6FQMPXZ5KXTGTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the interpolation with the potential bound for global solutions of the defocusing cubic wave equation on T2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tristan Roy","submitted_at":"2014-11-22T16:52:02Z","abstract_excerpt":"We prove that the solutions of the defocusing cubic wave equation on T2 exist globally in time in Hs(T2) for s > 2/5 by contradiction. Assuming that one of the maximal times of existence is finite, we prove that the Sobolev norm of each of these solutions is bounded in an open neighborhood of it by estimating the growth of a mollified energy through the interpolation with the potential bound for the low frequency part."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6141","kind":"arxiv","version":4},"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":"2026-05-18T01:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJcAHmX9xUHoJuEFIjHakczKcg9BRtCj/cEeudGQ/w+p+3pfkO5NNhr34ymA92zXUPiP41neTakmJa+mj8+mAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:40:39.599481Z"},"content_sha256":"55438c4ffa7dd227bcb46af32c90c43ff68d7b4d1dc0b239ad8b4676a261d672","schema_version":"1.0","event_id":"sha256:55438c4ffa7dd227bcb46af32c90c43ff68d7b4d1dc0b239ad8b4676a261d672"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSHLMB5K46QG6FQMPXZ5KXTGTT/bundle.json","state_url":"https://pith.science/pith/XSHLMB5K46QG6FQMPXZ5KXTGTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSHLMB5K46QG6FQMPXZ5KXTGTT/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":"2026-06-03T18:40:39Z","links":{"resolver":"https://pith.science/pith/XSHLMB5K46QG6FQMPXZ5KXTGTT","bundle":"https://pith.science/pith/XSHLMB5K46QG6FQMPXZ5KXTGTT/bundle.json","state":"https://pith.science/pith/XSHLMB5K46QG6FQMPXZ5KXTGTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSHLMB5K46QG6FQMPXZ5KXTGTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XSHLMB5K46QG6FQMPXZ5KXTGTT","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":"ba0d095bb1534d98b2ff7815097ac0e0f709ee57d8c3913f2a0e30dc71e3a77d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-22T16:52:02Z","title_canon_sha256":"491c0bb15656ad87f3e134cf10c5e2a78957f9478876617d168b563a4cdad43d"},"schema_version":"1.0","source":{"id":"1411.6141","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6141","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6141v4","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6141","created_at":"2026-05-18T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"XSHLMB5K46QG","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XSHLMB5K46QG6FQM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XSHLMB5K","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:55438c4ffa7dd227bcb46af32c90c43ff68d7b4d1dc0b239ad8b4676a261d672","target":"graph","created_at":"2026-05-18T01:15:58Z","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 prove that the solutions of the defocusing cubic wave equation on T2 exist globally in time in Hs(T2) for s > 2/5 by contradiction. Assuming that one of the maximal times of existence is finite, we prove that the Sobolev norm of each of these solutions is bounded in an open neighborhood of it by estimating the growth of a mollified energy through the interpolation with the potential bound for the low frequency part.","authors_text":"Tristan Roy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-22T16:52:02Z","title":"On the interpolation with the potential bound for global solutions of the defocusing cubic wave equation on T2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6141","kind":"arxiv","version":4},"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":"sha256:1e3598cc59cc6bbc42c8e860fc2a1be2cba7d7182cf58de019fd7400d223340f","target":"record","created_at":"2026-05-18T01:15:58Z","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":"ba0d095bb1534d98b2ff7815097ac0e0f709ee57d8c3913f2a0e30dc71e3a77d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-22T16:52:02Z","title_canon_sha256":"491c0bb15656ad87f3e134cf10c5e2a78957f9478876617d168b563a4cdad43d"},"schema_version":"1.0","source":{"id":"1411.6141","kind":"arxiv","version":4}},"canonical_sha256":"bc8eb607aae7a06f160c7df3d55e669ce65dc248b830fea8005a116447f2f9b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc8eb607aae7a06f160c7df3d55e669ce65dc248b830fea8005a116447f2f9b2","first_computed_at":"2026-05-18T01:15:58.972565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:58.972565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xXVAAdZ6Kei6AxjGBBUmKxcgy3N0cGKo1OutNvfOckSG+yyAVmZW7n2xN5dBSCP7mWDtoauGcNFurHe863wOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:58.973238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6141","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e3598cc59cc6bbc42c8e860fc2a1be2cba7d7182cf58de019fd7400d223340f","sha256:55438c4ffa7dd227bcb46af32c90c43ff68d7b4d1dc0b239ad8b4676a261d672"],"state_sha256":"7830cb6d05b10d5f0f35e01d7eba13d972e86672e2eb31b8b05597f77682c341"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tU5Kb3fd+zIj46JUOHKTov6k7HmRVSD6RluPls3YUyVaVeMFJaR7gIiWO7wwdc5T0rmJJ5Cfj1AtCLlRm/7QDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:40:39.601435Z","bundle_sha256":"fe58779e5fde04a07ef80eac15c56d0783aa98c14bdd3adc75deb966f040d3df"}}