Pith Number

pith:MMO3MQ6E

pith:2026:MMO3MQ6EIDQYPZZZXSOJ54ZOBK

not attested not anchored not stored refs pending

Schur Visibility and Anti-Phantom Reduction in One-Component Navier-Stokes Degeneration

Runlong Yu

arxiv:2606.12267 v1 · 2026-06-10 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MMO3MQ6EIDQYPZZZXSOJ54ZOBK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

3 papers in Pith

Finite-Window Recursive Audit Chains for Navier-Stokes Generated Packages

Finite-Chain CKN-Bad Scale Counting for Navier-Stokes: Standard PDE Closure and Canonical Detector Realization

A Structural Audit of Navier-Stokes Obstruction Calculus

Receipt and verification

First computed	2026-06-11T01:10:58.767742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

631db643c440e187e739bc9c9ef32e0aa2d9e3ca76104df4868da145db98628b

Aliases

arxiv: 2606.12267 · arxiv_version: 2606.12267v1 · doi: 10.48550/arxiv.2606.12267 · pith_short_12: MMO3MQ6EIDQY · pith_short_16: MMO3MQ6EIDQYPZZZ · pith_short_8: MMO3MQ6E

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MMO3MQ6EIDQYPZZZXSOJ54ZOBK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 631db643c440e187e739bc9c9ef32e0aa2d9e3ca76104df4868da145db98628b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d969fa5a9cfbc775209bbfc82f759c7a626e12c7300084347a3c9248a47f1453",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-10T16:11:09Z",
    "title_canon_sha256": "f7d3192f03af051a701ae25b2e784fa8e33e19589efe7a62070cff2348875c12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12267",
    "kind": "arxiv",
    "version": 1
  }
}