Pith Number

pith:LGYNMA4H

pith:2026:LGYNMA4HLHNXFFLZOOQJWBV56O

not attested not anchored not stored refs pending

The subsonic limit of the 3D Zakharov system

Jia Shen, Rui Jia, Yifei Wu

arxiv:2607.12685 v1 · 2026-07-14 · 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{LGYNMA4HLHNXFFLZOOQJWBV56O}

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	2026-07-15T01:22:12.061986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59b0d6038759db72957973a09b06bdf3a2da00a858c16a6165241abebc752809

Aliases

arxiv: 2607.12685 · arxiv_version: 2607.12685v1 · doi: 10.48550/arxiv.2607.12685 · pith_short_12: LGYNMA4HLHNX · pith_short_16: LGYNMA4HLHNXFFLZ · pith_short_8: LGYNMA4H

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/LGYNMA4HLHNXFFLZOOQJWBV56O \
  | 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: 59b0d6038759db72957973a09b06bdf3a2da00a858c16a6165241abebc752809

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d5b0b3773088c19faf77557833c1c2dc21d56e78ba3ec1b1d648da0da95bc3e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-14T12:10:58Z",
    "title_canon_sha256": "4a7b9f5dfaa842a93c5698a7933b323da7485593077e3681045480174aad427b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12685",
    "kind": "arxiv",
    "version": 1
  }
}