{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TR3J7IOI63VDQSP3HOHPOLJPTP","short_pith_number":"pith:TR3J7IOI","canonical_record":{"source":{"id":"1202.0718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-03T14:41:14Z","cross_cats_sorted":[],"title_canon_sha256":"35c394762964fd88de9c84df881ae92b0ec5f70f811ce012a1d683c615840964","abstract_canon_sha256":"692780f77cc9e3c4019d4af90970ae87fafc2dd019e2151ddf242c2486af0edd"},"schema_version":"1.0"},"canonical_sha256":"9c769fa1c8f6ea3849fb3b8ef72d2f9beee2da63e5c9583a0f717c7b6ec9db0a","source":{"kind":"arxiv","id":"1202.0718","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0718","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0718v1","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0718","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"TR3J7IOI63VD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TR3J7IOI63VDQSP3","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TR3J7IOI","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TR3J7IOI63VDQSP3HOHPOLJPTP","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-03T14:41:14Z","cross_cats_sorted":[],"title_canon_sha256":"35c394762964fd88de9c84df881ae92b0ec5f70f811ce012a1d683c615840964","abstract_canon_sha256":"692780f77cc9e3c4019d4af90970ae87fafc2dd019e2151ddf242c2486af0edd"},"schema_version":"1.0"},"canonical_sha256":"9c769fa1c8f6ea3849fb3b8ef72d2f9beee2da63e5c9583a0f717c7b6ec9db0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:08.822544Z","signature_b64":"tVBuXSxxvXiDz6047sQW/WMVjJq7JAbPC909BkjSailH3keLP9UsvZacXgPWma4c2XeWfmn6JGrj/rQ4S8BgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c769fa1c8f6ea3849fb3b8ef72d2f9beee2da63e5c9583a0f717c7b6ec9db0a","last_reissued_at":"2026-05-18T03:14:08.822068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:08.822068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0718","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":"2026-05-18T03:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oeCSLuMvWS8kzzn+gA2aEUapqLVdOy9Q9Aj3kPF9OsUarqMBgk6A8ClJjcCcELt5z8gFTAARYBY9FifDwYo0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:14:45.483880Z"},"content_sha256":"966328b106afd7020dadcff0170975e1bb133340ff75f0b7a1db9ed8f9c80b12","schema_version":"1.0","event_id":"sha256:966328b106afd7020dadcff0170975e1bb133340ff75f0b7a1db9ed8f9c80b12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TR3J7IOI63VDQSP3HOHPOLJPTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lorenzo Brandolese (ICJ)","submitted_at":"2012-02-03T14:41:14Z","abstract_excerpt":"We exhibit a sufficient condition in terms of decay at infinity of the initial data for the finite time blowup of strong solutions to the Camassa--Holm equation: a wave breaking will occur as soon as the initial data decay faster at infinity than the solitons. In the case of data decaying slower than solitons we provide persistence results for the solution in weighted $L^p$-spaces, for a large class of moderate weights. Explicit asymptotic profiles illustrate the optimality of these results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0718","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":"2026-05-18T03:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"anedU+XM0cagGo6tlD90QVKMxEP3QScII/oAr+0+zAt9QHtY2S8VUxLpPzH8ZPn7rWUfb8dSSjqFZ1oAIYpFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:14:45.484546Z"},"content_sha256":"19ed877f76b48c3f3fb28ada5eea3ce790a91a0ea56daa15a1ac4cfd55b8618e","schema_version":"1.0","event_id":"sha256:19ed877f76b48c3f3fb28ada5eea3ce790a91a0ea56daa15a1ac4cfd55b8618e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TR3J7IOI63VDQSP3HOHPOLJPTP/bundle.json","state_url":"https://pith.science/pith/TR3J7IOI63VDQSP3HOHPOLJPTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TR3J7IOI63VDQSP3HOHPOLJPTP/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":"2026-06-07T09:14:45Z","links":{"resolver":"https://pith.science/pith/TR3J7IOI63VDQSP3HOHPOLJPTP","bundle":"https://pith.science/pith/TR3J7IOI63VDQSP3HOHPOLJPTP/bundle.json","state":"https://pith.science/pith/TR3J7IOI63VDQSP3HOHPOLJPTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TR3J7IOI63VDQSP3HOHPOLJPTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TR3J7IOI63VDQSP3HOHPOLJPTP","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":"692780f77cc9e3c4019d4af90970ae87fafc2dd019e2151ddf242c2486af0edd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-03T14:41:14Z","title_canon_sha256":"35c394762964fd88de9c84df881ae92b0ec5f70f811ce012a1d683c615840964"},"schema_version":"1.0","source":{"id":"1202.0718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0718","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0718v1","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0718","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"TR3J7IOI63VD","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TR3J7IOI63VDQSP3","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TR3J7IOI","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:19ed877f76b48c3f3fb28ada5eea3ce790a91a0ea56daa15a1ac4cfd55b8618e","target":"graph","created_at":"2026-05-18T03:14:08Z","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 exhibit a sufficient condition in terms of decay at infinity of the initial data for the finite time blowup of strong solutions to the Camassa--Holm equation: a wave breaking will occur as soon as the initial data decay faster at infinity than the solitons. In the case of data decaying slower than solitons we provide persistence results for the solution in weighted $L^p$-spaces, for a large class of moderate weights. Explicit asymptotic profiles illustrate the optimality of these results.","authors_text":"Lorenzo Brandolese (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-03T14:41:14Z","title":"Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0718","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":"sha256:966328b106afd7020dadcff0170975e1bb133340ff75f0b7a1db9ed8f9c80b12","target":"record","created_at":"2026-05-18T03:14:08Z","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":"692780f77cc9e3c4019d4af90970ae87fafc2dd019e2151ddf242c2486af0edd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-03T14:41:14Z","title_canon_sha256":"35c394762964fd88de9c84df881ae92b0ec5f70f811ce012a1d683c615840964"},"schema_version":"1.0","source":{"id":"1202.0718","kind":"arxiv","version":1}},"canonical_sha256":"9c769fa1c8f6ea3849fb3b8ef72d2f9beee2da63e5c9583a0f717c7b6ec9db0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c769fa1c8f6ea3849fb3b8ef72d2f9beee2da63e5c9583a0f717c7b6ec9db0a","first_computed_at":"2026-05-18T03:14:08.822068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:08.822068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tVBuXSxxvXiDz6047sQW/WMVjJq7JAbPC909BkjSailH3keLP9UsvZacXgPWma4c2XeWfmn6JGrj/rQ4S8BgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:08.822544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:966328b106afd7020dadcff0170975e1bb133340ff75f0b7a1db9ed8f9c80b12","sha256:19ed877f76b48c3f3fb28ada5eea3ce790a91a0ea56daa15a1ac4cfd55b8618e"],"state_sha256":"827a2f5b20ef0461e75660a2e2272ea628a4740d7a9b6edbc957aefeebee8638"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0RrH/ozXbD+poc1EpJNUFCra4Kqzz/IqNwxOStxskPtEi7GlQtqwDWs9rYlvnK8SlUvkg2e2p2SqpLTqH3dUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:14:45.487787Z","bundle_sha256":"014af6d6214f13476d646598a7c13792c2579fe25a4f1f39ce387b326f40f0c1"}}