{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YQTTWRDWVDBRVZCWN6EFUUOTUT","short_pith_number":"pith:YQTTWRDW","canonical_record":{"source":{"id":"0906.3384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-06-18T09:19:52Z","cross_cats_sorted":[],"title_canon_sha256":"14208c3e40b2fad4346c07ab9dbae0b2a03cefa855455209e6858b5329c7943c","abstract_canon_sha256":"37014f8183817b0ec180ea5b3ae8df88377b5c9ec4b87dee10d776822abde694"},"schema_version":"1.0"},"canonical_sha256":"c4273b4476a8c31ae4566f885a51d3a4d44d8eda3fb8f9d6000252bf0f14af33","source":{"kind":"arxiv","id":"0906.3384","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3384","created_at":"2026-05-18T02:13:19Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3384v1","created_at":"2026-05-18T02:13:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3384","created_at":"2026-05-18T02:13:19Z"},{"alias_kind":"pith_short_12","alias_value":"YQTTWRDWVDBR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YQTTWRDWVDBRVZCW","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YQTTWRDW","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YQTTWRDWVDBRVZCWN6EFUUOTUT","target":"record","payload":{"canonical_record":{"source":{"id":"0906.3384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-06-18T09:19:52Z","cross_cats_sorted":[],"title_canon_sha256":"14208c3e40b2fad4346c07ab9dbae0b2a03cefa855455209e6858b5329c7943c","abstract_canon_sha256":"37014f8183817b0ec180ea5b3ae8df88377b5c9ec4b87dee10d776822abde694"},"schema_version":"1.0"},"canonical_sha256":"c4273b4476a8c31ae4566f885a51d3a4d44d8eda3fb8f9d6000252bf0f14af33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:19.163850Z","signature_b64":"qz8fOAaD8uNuzon8WyMi2lFC1hmuMKaiv2Qs0xsGk2Xagu1npLN7dUktv2AathqzR+rQH/UpuyxwqG4kmti+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4273b4476a8c31ae4566f885a51d3a4d44d8eda3fb8f9d6000252bf0f14af33","last_reissued_at":"2026-05-18T02:13:19.163168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:19.163168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.3384","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":"2026-05-18T02:13:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"htI7yB7qU+OMmUc6ocDhhsZmn8G3pZgWWE2YDJeCtCib3bQAYakyLXg9hfHAJUNR1QVt+L3qbH6ZLXNgyZJ5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:00:48.721588Z"},"content_sha256":"d59250e02713de23c9c7a8e5fd25713f653303b064b61df277f23ba833ce05f0","schema_version":"1.0","event_id":"sha256:d59250e02713de23c9c7a8e5fd25713f653303b064b61df277f23ba833ce05f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YQTTWRDWVDBRVZCWN6EFUUOTUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy dispersed large data wave maps in 2+1 dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Tataru, Jacob Sterbenz","submitted_at":"2009-06-18T09:19:52Z","abstract_excerpt":"In this article we consider large data Wave-Maps from $\\mathbb{R}^{2+1}$ into a compact Riemannian manifold $(\\mathcal{M},g)$, and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (non-dispersive) concentration is absent. In a companion article we use these results in order to establish a full regularity theory for large data Wave-Maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3384","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":"2026-05-18T02:13:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"glW4gbMLZ+RuxEQrC+/ARlUCEPcQPwa9lRwRlwPCjej7NWpPAx4X2o2rRzK1jg0mNKKNzDvJAkBCGjkSKw6CDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:00:48.722226Z"},"content_sha256":"9604d5138c7dcd81d63e9eb87d775119f2ee6ecc9d5f53d94f5f56805eb410ee","schema_version":"1.0","event_id":"sha256:9604d5138c7dcd81d63e9eb87d775119f2ee6ecc9d5f53d94f5f56805eb410ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YQTTWRDWVDBRVZCWN6EFUUOTUT/bundle.json","state_url":"https://pith.science/pith/YQTTWRDWVDBRVZCWN6EFUUOTUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YQTTWRDWVDBRVZCWN6EFUUOTUT/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":"2026-06-11T02:00:48Z","links":{"resolver":"https://pith.science/pith/YQTTWRDWVDBRVZCWN6EFUUOTUT","bundle":"https://pith.science/pith/YQTTWRDWVDBRVZCWN6EFUUOTUT/bundle.json","state":"https://pith.science/pith/YQTTWRDWVDBRVZCWN6EFUUOTUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YQTTWRDWVDBRVZCWN6EFUUOTUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YQTTWRDWVDBRVZCWN6EFUUOTUT","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":"37014f8183817b0ec180ea5b3ae8df88377b5c9ec4b87dee10d776822abde694","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-06-18T09:19:52Z","title_canon_sha256":"14208c3e40b2fad4346c07ab9dbae0b2a03cefa855455209e6858b5329c7943c"},"schema_version":"1.0","source":{"id":"0906.3384","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.3384","created_at":"2026-05-18T02:13:19Z"},{"alias_kind":"arxiv_version","alias_value":"0906.3384v1","created_at":"2026-05-18T02:13:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.3384","created_at":"2026-05-18T02:13:19Z"},{"alias_kind":"pith_short_12","alias_value":"YQTTWRDWVDBR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YQTTWRDWVDBRVZCW","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YQTTWRDW","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:9604d5138c7dcd81d63e9eb87d775119f2ee6ecc9d5f53d94f5f56805eb410ee","target":"graph","created_at":"2026-05-18T02:13:19Z","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 article we consider large data Wave-Maps from $\\mathbb{R}^{2+1}$ into a compact Riemannian manifold $(\\mathcal{M},g)$, and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (non-dispersive) concentration is absent. In a companion article we use these results in order to establish a full regularity theory for large data Wave-Maps.","authors_text":"Daniel Tataru, Jacob Sterbenz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-06-18T09:19:52Z","title":"Energy dispersed large data wave maps in 2+1 dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3384","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:d59250e02713de23c9c7a8e5fd25713f653303b064b61df277f23ba833ce05f0","target":"record","created_at":"2026-05-18T02:13:19Z","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":"37014f8183817b0ec180ea5b3ae8df88377b5c9ec4b87dee10d776822abde694","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-06-18T09:19:52Z","title_canon_sha256":"14208c3e40b2fad4346c07ab9dbae0b2a03cefa855455209e6858b5329c7943c"},"schema_version":"1.0","source":{"id":"0906.3384","kind":"arxiv","version":1}},"canonical_sha256":"c4273b4476a8c31ae4566f885a51d3a4d44d8eda3fb8f9d6000252bf0f14af33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4273b4476a8c31ae4566f885a51d3a4d44d8eda3fb8f9d6000252bf0f14af33","first_computed_at":"2026-05-18T02:13:19.163168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:19.163168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qz8fOAaD8uNuzon8WyMi2lFC1hmuMKaiv2Qs0xsGk2Xagu1npLN7dUktv2AathqzR+rQH/UpuyxwqG4kmti+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:19.163850Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.3384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d59250e02713de23c9c7a8e5fd25713f653303b064b61df277f23ba833ce05f0","sha256:9604d5138c7dcd81d63e9eb87d775119f2ee6ecc9d5f53d94f5f56805eb410ee"],"state_sha256":"e4654d10c9e2307e462b95efa6477ed0c398036c9bd7b2b1613135eb491d3e69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rWeXVRXX+7kvvczQBOTW7iG1/N4nscAnFS7032P8qEsZWefM3+ZigHp2WBiMF07lhXV0MkkF30V9nQ6i2v7oBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:00:48.725747Z","bundle_sha256":"5bc210ca714bd1f24053f2d7596ae4393be4e6c156762d704461043e59d2d5da"}}