{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MBQKKDTQTLWTQBRAVDPOHOVDGA","short_pith_number":"pith:MBQKKDTQ","canonical_record":{"source":{"id":"1210.2602","kind":"arxiv","version":11},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-09T14:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"360e0b4081dac546dad8d3ffb43167eaf758bd44115bfa58d0c183959e9c26d0","abstract_canon_sha256":"6f7e6dfdc3aefce42a94c1927191ec83c2c8a38711e01fc34ae9a6a3382d34fb"},"schema_version":"1.0"},"canonical_sha256":"6060a50e709aed380620a8dee3baa330380e834490a645c21ece2d712d2a8710","source":{"kind":"arxiv","id":"1210.2602","version":11},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2602","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2602v11","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2602","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"MBQKKDTQTLWT","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MBQKKDTQTLWTQBRA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MBQKKDTQ","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MBQKKDTQTLWTQBRAVDPOHOVDGA","target":"record","payload":{"canonical_record":{"source":{"id":"1210.2602","kind":"arxiv","version":11},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-09T14:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"360e0b4081dac546dad8d3ffb43167eaf758bd44115bfa58d0c183959e9c26d0","abstract_canon_sha256":"6f7e6dfdc3aefce42a94c1927191ec83c2c8a38711e01fc34ae9a6a3382d34fb"},"schema_version":"1.0"},"canonical_sha256":"6060a50e709aed380620a8dee3baa330380e834490a645c21ece2d712d2a8710","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:43.038993Z","signature_b64":"QZEa6N4utdwiFN3LnEcgoTH/z48GQdZym8bu8UWQ/NrdKj/rkwJGaMBv7DAY4brSxZ5UUE/HTbWnyH6XfM6pCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6060a50e709aed380620a8dee3baa330380e834490a645c21ece2d712d2a8710","last_reissued_at":"2026-05-18T03:06:43.038569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:43.038569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.2602","source_version":11,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0Si5aP2y5xzuYDEZCNRlmvUbT5zVTBEfcL8hLgJgpp0KeJI6H07RqCAMed3vnRQUO38EY/KWtpQ1tfIogygAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:55:08.050688Z"},"content_sha256":"9f6a732e52b6a6c610b65315475fbbdeb87b018ee7275e724e4ce305e9ceb854","schema_version":"1.0","event_id":"sha256:9f6a732e52b6a6c610b65315475fbbdeb87b018ee7275e724e4ce305e9ceb854"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MBQKKDTQTLWTQBRAVDPOHOVDGA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the multivariate Burgers equation and the incompressible Navier-Stokes equation (part III)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joerg Kampen","submitted_at":"2012-10-09T14:06:44Z","abstract_excerpt":"In this paper we first obtain local contraction results in a Hm-norm with respect to time and space for a local scheme. We show that a global controlled scheme preserves higher order regularity with respect to the spatial variables together with polynomial decay of order m of the data at each time step. Here, we simplify the controlled scheme considered in [1] and [2]. Especially, for the simplified controlled scheme we get an upper bound for the Leray projection term. Furthermore, the schemes discussed in [1] and [2] are simplified in the sense that the estimates are achieved without the use "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2602","kind":"arxiv","version":11},"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":"2026-05-18T03:06:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YXxPv/oIojS/IMKNGZodRi7xpcyi8qaGtUPURqYM0qSklEERO5v1rWXzMWa4MgzAFgCgIsYKOiAMFczresO+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:55:08.051106Z"},"content_sha256":"c846e87356bc3a031f0c6fa941f58e4d1a83afdf96058cfe751b28274b676b71","schema_version":"1.0","event_id":"sha256:c846e87356bc3a031f0c6fa941f58e4d1a83afdf96058cfe751b28274b676b71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MBQKKDTQTLWTQBRAVDPOHOVDGA/bundle.json","state_url":"https://pith.science/pith/MBQKKDTQTLWTQBRAVDPOHOVDGA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MBQKKDTQTLWTQBRAVDPOHOVDGA/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":"2026-06-04T11:55:08Z","links":{"resolver":"https://pith.science/pith/MBQKKDTQTLWTQBRAVDPOHOVDGA","bundle":"https://pith.science/pith/MBQKKDTQTLWTQBRAVDPOHOVDGA/bundle.json","state":"https://pith.science/pith/MBQKKDTQTLWTQBRAVDPOHOVDGA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MBQKKDTQTLWTQBRAVDPOHOVDGA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MBQKKDTQTLWTQBRAVDPOHOVDGA","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":"6f7e6dfdc3aefce42a94c1927191ec83c2c8a38711e01fc34ae9a6a3382d34fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-09T14:06:44Z","title_canon_sha256":"360e0b4081dac546dad8d3ffb43167eaf758bd44115bfa58d0c183959e9c26d0"},"schema_version":"1.0","source":{"id":"1210.2602","kind":"arxiv","version":11}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2602","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2602v11","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2602","created_at":"2026-05-18T03:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"MBQKKDTQTLWT","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MBQKKDTQTLWTQBRA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MBQKKDTQ","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:c846e87356bc3a031f0c6fa941f58e4d1a83afdf96058cfe751b28274b676b71","target":"graph","created_at":"2026-05-18T03:06:43Z","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 first obtain local contraction results in a Hm-norm with respect to time and space for a local scheme. We show that a global controlled scheme preserves higher order regularity with respect to the spatial variables together with polynomial decay of order m of the data at each time step. Here, we simplify the controlled scheme considered in [1] and [2]. Especially, for the simplified controlled scheme we get an upper bound for the Leray projection term. Furthermore, the schemes discussed in [1] and [2] are simplified in the sense that the estimates are achieved without the use ","authors_text":"Joerg Kampen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-09T14:06:44Z","title":"On the multivariate Burgers equation and the incompressible Navier-Stokes equation (part III)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2602","kind":"arxiv","version":11},"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":"sha256:9f6a732e52b6a6c610b65315475fbbdeb87b018ee7275e724e4ce305e9ceb854","target":"record","created_at":"2026-05-18T03:06:43Z","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":"6f7e6dfdc3aefce42a94c1927191ec83c2c8a38711e01fc34ae9a6a3382d34fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-09T14:06:44Z","title_canon_sha256":"360e0b4081dac546dad8d3ffb43167eaf758bd44115bfa58d0c183959e9c26d0"},"schema_version":"1.0","source":{"id":"1210.2602","kind":"arxiv","version":11}},"canonical_sha256":"6060a50e709aed380620a8dee3baa330380e834490a645c21ece2d712d2a8710","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6060a50e709aed380620a8dee3baa330380e834490a645c21ece2d712d2a8710","first_computed_at":"2026-05-18T03:06:43.038569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:43.038569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZEa6N4utdwiFN3LnEcgoTH/z48GQdZym8bu8UWQ/NrdKj/rkwJGaMBv7DAY4brSxZ5UUE/HTbWnyH6XfM6pCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:43.038993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2602","source_kind":"arxiv","source_version":11}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f6a732e52b6a6c610b65315475fbbdeb87b018ee7275e724e4ce305e9ceb854","sha256:c846e87356bc3a031f0c6fa941f58e4d1a83afdf96058cfe751b28274b676b71"],"state_sha256":"acde5580bf134df9f17ccb21306af918f4d9f58d91820c8b533f59910362ffc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E4tkaOgKQbD561f2A3RcEliyfuOwrFZa8CyADkETrh4roNvSysJPjJprWQfdL7FkLcVRH3pvuMJh8OYJUR+ADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T11:55:08.053281Z","bundle_sha256":"17a651e2812795452baa1742f1f98f35731ffce1ddcc25c3e10b2f0bc5280b6e"}}