{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:B3ADGNMWKXJH5MF2FKOUNIL34Z","short_pith_number":"pith:B3ADGNMW","canonical_record":{"source":{"id":"2606.11720","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-10T06:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"d676d21ea2f6fca7aaacbd3de78ddf2575051a5720abf7be09f1cfee22658cf8","abstract_canon_sha256":"39ab28acdc404eca0c66367b7f72a063a800075c6ee3eddc1ab1e6ce10ab5747"},"schema_version":"1.0"},"canonical_sha256":"0ec033359655d27eb0ba2a9d46a17be66cee640f0cd4f69b8dda08a2ac465db8","source":{"kind":"arxiv","id":"2606.11720","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11720","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11720v1","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11720","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"B3ADGNMWKXJH","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"pith_short_16","alias_value":"B3ADGNMWKXJH5MF2","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"pith_short_8","alias_value":"B3ADGNMW","created_at":"2026-06-11T01:10:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:B3ADGNMWKXJH5MF2FKOUNIL34Z","target":"record","payload":{"canonical_record":{"source":{"id":"2606.11720","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-10T06:50:04Z","cross_cats_sorted":[],"title_canon_sha256":"d676d21ea2f6fca7aaacbd3de78ddf2575051a5720abf7be09f1cfee22658cf8","abstract_canon_sha256":"39ab28acdc404eca0c66367b7f72a063a800075c6ee3eddc1ab1e6ce10ab5747"},"schema_version":"1.0"},"canonical_sha256":"0ec033359655d27eb0ba2a9d46a17be66cee640f0cd4f69b8dda08a2ac465db8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:10:04.639196Z","signature_b64":"Gjm6KU8uuHw3nMjCmIRiD90dr0WzrDk3kXadVmF0dHH725+RYm2oW3ElttbpvUD/oYPejsFc15ec73WDsXjECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ec033359655d27eb0ba2a9d46a17be66cee640f0cd4f69b8dda08a2ac465db8","last_reissued_at":"2026-06-11T01:10:04.638287Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:10:04.638287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.11720","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":"2026-06-11T01:10:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bfd75Fy55KUAB7WJjEkzBgFROq8ZPluugExmBZtD/glTRddf13RWhYnBrAsdmwch87TVhmXyoV+J8d8k1GsSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:19:17.205791Z"},"content_sha256":"10a42e6f32048d79ef29ea5784df33f6de32927de31f6b7b2a37c070ff5001ae","schema_version":"1.0","event_id":"sha256:10a42e6f32048d79ef29ea5784df33f6de32927de31f6b7b2a37c070ff5001ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:B3ADGNMWKXJH5MF2FKOUNIL34Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strict 2.5D Shadows for One-Component Navier-Stokes Regularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Runlong Yu","submitted_at":"2026-06-10T06:50:04Z","abstract_excerpt":"We formulate and prove a conditional finite-scale reduction theorem for the local one-component regularity problem for suitable weak solutions of the three-dimensional Navier--Stokes equations. Starting from a scale-invariant bound Phi(1) <= M and smallness of the critical vertical component C_3(1) = delta, the argument compares the solution with a strict two-and-a-half-dimensional shadow class. The comparison is made in the harmonic-pressure quotient, which is the natural local topology for pressure compactness. The Reynolds commutator produced by coarse graining is treated as a positive cova"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11720","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11720/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-11T01:10:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nlK+dRxyVW6t3nl1r9zZqHxRDRgeJEtX1BEC62zkC/zC1TmIUcx4J5mJQxeICvRFYDsgCrWs+FO+PwPVQPJcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:19:17.206162Z"},"content_sha256":"d4f7ab055d9214a41f1de83f3bbc341f6b89c8d5f94f9ee792d8586f0365c1d4","schema_version":"1.0","event_id":"sha256:d4f7ab055d9214a41f1de83f3bbc341f6b89c8d5f94f9ee792d8586f0365c1d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3ADGNMWKXJH5MF2FKOUNIL34Z/bundle.json","state_url":"https://pith.science/pith/B3ADGNMWKXJH5MF2FKOUNIL34Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3ADGNMWKXJH5MF2FKOUNIL34Z/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":"2026-06-28T09:19:17Z","links":{"resolver":"https://pith.science/pith/B3ADGNMWKXJH5MF2FKOUNIL34Z","bundle":"https://pith.science/pith/B3ADGNMWKXJH5MF2FKOUNIL34Z/bundle.json","state":"https://pith.science/pith/B3ADGNMWKXJH5MF2FKOUNIL34Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3ADGNMWKXJH5MF2FKOUNIL34Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:B3ADGNMWKXJH5MF2FKOUNIL34Z","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":"39ab28acdc404eca0c66367b7f72a063a800075c6ee3eddc1ab1e6ce10ab5747","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-10T06:50:04Z","title_canon_sha256":"d676d21ea2f6fca7aaacbd3de78ddf2575051a5720abf7be09f1cfee22658cf8"},"schema_version":"1.0","source":{"id":"2606.11720","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11720","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11720v1","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11720","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"B3ADGNMWKXJH","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"pith_short_16","alias_value":"B3ADGNMWKXJH5MF2","created_at":"2026-06-11T01:10:04Z"},{"alias_kind":"pith_short_8","alias_value":"B3ADGNMW","created_at":"2026-06-11T01:10:04Z"}],"graph_snapshots":[{"event_id":"sha256:d4f7ab055d9214a41f1de83f3bbc341f6b89c8d5f94f9ee792d8586f0365c1d4","target":"graph","created_at":"2026-06-11T01:10:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.11720/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We formulate and prove a conditional finite-scale reduction theorem for the local one-component regularity problem for suitable weak solutions of the three-dimensional Navier--Stokes equations. Starting from a scale-invariant bound Phi(1) <= M and smallness of the critical vertical component C_3(1) = delta, the argument compares the solution with a strict two-and-a-half-dimensional shadow class. The comparison is made in the harmonic-pressure quotient, which is the natural local topology for pressure compactness. The Reynolds commutator produced by coarse graining is treated as a positive cova","authors_text":"Runlong Yu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-10T06:50:04Z","title":"Strict 2.5D Shadows for One-Component Navier-Stokes Regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11720","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":"sha256:10a42e6f32048d79ef29ea5784df33f6de32927de31f6b7b2a37c070ff5001ae","target":"record","created_at":"2026-06-11T01:10:04Z","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":"39ab28acdc404eca0c66367b7f72a063a800075c6ee3eddc1ab1e6ce10ab5747","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-10T06:50:04Z","title_canon_sha256":"d676d21ea2f6fca7aaacbd3de78ddf2575051a5720abf7be09f1cfee22658cf8"},"schema_version":"1.0","source":{"id":"2606.11720","kind":"arxiv","version":1}},"canonical_sha256":"0ec033359655d27eb0ba2a9d46a17be66cee640f0cd4f69b8dda08a2ac465db8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ec033359655d27eb0ba2a9d46a17be66cee640f0cd4f69b8dda08a2ac465db8","first_computed_at":"2026-06-11T01:10:04.638287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:04.638287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gjm6KU8uuHw3nMjCmIRiD90dr0WzrDk3kXadVmF0dHH725+RYm2oW3ElttbpvUD/oYPejsFc15ec73WDsXjECg==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:04.639196Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11720","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10a42e6f32048d79ef29ea5784df33f6de32927de31f6b7b2a37c070ff5001ae","sha256:d4f7ab055d9214a41f1de83f3bbc341f6b89c8d5f94f9ee792d8586f0365c1d4"],"state_sha256":"2dc10ab3f259f9a51a3569fc4f34d8b8200ef89c1bf1c067d7e7d964300b3a77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnVLACvpm6ESnq7jKtCeYC38vdC6HC7fspfpS5Fp6Z7gqqld3ADoNnUsxSsLuKD9V3ZmAiEJaaxakiJd8JwABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T09:19:17.208135Z","bundle_sha256":"a5919babcf076ad4928214c7cebbcacaedf3a5f44bce246a94ed87c7e36a6b91"}}