Pith Number

pith:DO33O7UV

pith:2021:DO33O7UV4N6BDZSJ6RGEMUOXSQ

not attested not anchored not stored refs pending

Global well-posedness of $z$-weak solutions to the primitive equations without vertical diffusivity

Guozhi Yuan, Jinkai Li

arxiv:2107.07688 v1 · 2021-07-16 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DO33O7UV4N6BDZSJ6RGEMUOXSQ}

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	2026-07-05T03:57:09.631137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bb7b77e95e37c11e649f44c4651d794307ecd469a1bf8b27df6cd18b0b5bf81

Aliases

arxiv: 2107.07688 · arxiv_version: 2107.07688v1 · doi: 10.48550/arxiv.2107.07688 · pith_short_12: DO33O7UV4N6B · pith_short_16: DO33O7UV4N6BDZSJ · pith_short_8: DO33O7UV

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/DO33O7UV4N6BDZSJ6RGEMUOXSQ \
  | 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: 1bb7b77e95e37c11e649f44c4651d794307ecd469a1bf8b27df6cd18b0b5bf81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa6ea205843b5cddf0122270adc6ba018920fc00e03a2912e9d87548730c8371",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-07-16T03:36:58Z",
    "title_canon_sha256": "263e7cc009824f3322cbb9a601f3a13e882de0fa9e1e339fcae2e0e82eea9f52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.07688",
    "kind": "arxiv",
    "version": 1
  }
}