Pith Number

pith:DMQ6FUJ5

pith:2026:DMQ6FUJ5YVRC5FEOBZZEUKGFJB

not attested not anchored not stored refs pending

Gravitational Enstrophy: Local Geometric Origin and Inverse-Cascade Constraints

Luis Lehner

arxiv:2608.03697 v1 · 2026-08-04 · gr-qc · astro-ph.HE · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DMQ6FUJ5YVRC5FEOBZZEUKGFJB}

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	2026-08-05T01:36:54.898747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b21e2d13dc5622e948e0e724a28c5484a24820998adafdcdcd25dbb73052be5

Aliases

arxiv: 2608.03697 · arxiv_version: 2608.03697v1 · doi: 10.48550/arxiv.2608.03697 · pith_short_12: DMQ6FUJ5YVRC · pith_short_16: DMQ6FUJ5YVRC5FEO · pith_short_8: DMQ6FUJ5

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/DMQ6FUJ5YVRC5FEOBZZEUKGFJB \
  | 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: 1b21e2d13dc5622e948e0e724a28c5484a24820998adafdcdcd25dbb73052be5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f36e1d626df624d56a152a499b1433cff9d22a327e28faf3446d810cc4b99113",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-08-04T14:01:20Z",
    "title_canon_sha256": "fbf913ee588721c0f08a3f3f1457a360aa3c4ffc771eaa76cd665fa9fd77c662"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.03697",
    "kind": "arxiv",
    "version": 1
  }
}