Pith Number

pith:ULTXV7OE

pith:2026:ULTXV7OE6K4NJ5DMXZYCHGGBZQ

not attested not anchored not stored refs pending

Coarse-Grained Resolution and Pressure-Flux Work Depletion for Navier-Stokes CKN Badness

Runlong Yu

arxiv:2606.25322 v1 · 2026-06-24 · 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{ULTXV7OE6K4NJ5DMXZYCHGGBZQ}

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.

Receipt and verification

First computed	2026-06-25T01:18:02.026723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2e77afdc4f2b8d4f46cbe702398c1cc3bf5102a0c67a63185af0cd773881962

Aliases

arxiv: 2606.25322 · arxiv_version: 2606.25322v1 · doi: 10.48550/arxiv.2606.25322 · pith_short_12: ULTXV7OE6K4N · pith_short_16: ULTXV7OE6K4NJ5DM · pith_short_8: ULTXV7OE

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/ULTXV7OE6K4NJ5DMXZYCHGGBZQ \
  | 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: a2e77afdc4f2b8d4f46cbe702398c1cc3bf5102a0c67a63185af0cd773881962

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef1a11bfc3109181a7e5ce0a37f410831d78a6efdc276d4a7af562b551bc6461",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-24T02:38:56Z",
    "title_canon_sha256": "a2e8edd2c885fc3617f4359136c9f7364aac1b8f0b5f37aef922216116690fcc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25322",
    "kind": "arxiv",
    "version": 1
  }
}