Pith Number

pith:XOOONUHE

pith:2026:XOOONUHEMJ6LGK7OAK2GYJG5P3

not attested not anchored not stored refs pending

Analytic Integration of the Lambert W Cosmic Fluid Model H(z) Formula

Ken Roberts, S. R. Valluri

arxiv:2608.07878 v1 · 2026-08-08 · math-ph · gr-qc · 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{XOOONUHEMJ6LGK7OAK2GYJG5P3}

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	2026-08-11T01:18:48.988068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb9ce6d0e4627cb32bee02b46c24dd7efee45421cbabdba55b211a5f29e0d82d

Aliases

arxiv: 2608.07878 · arxiv_version: 2608.07878v1 · doi: 10.48550/arxiv.2608.07878 · pith_short_12: XOOONUHEMJ6L · pith_short_16: XOOONUHEMJ6LGK7O · pith_short_8: XOOONUHE

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/XOOONUHEMJ6LGK7OAK2GYJG5P3 \
  | 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: bb9ce6d0e4627cb32bee02b46c24dd7efee45421cbabdba55b211a5f29e0d82d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfbcd8ddf141b5f34f1bde7fbad84b83e72ae2ece8b4ee8d91f6cc0d4eb39136",
    "cross_cats_sorted": [
      "gr-qc",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-08-08T03:07:36Z",
    "title_canon_sha256": "a7b965b6c81811e421c1370889d98a1ccfef59804cfb61a65c52a0089c230564"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07878",
    "kind": "arxiv",
    "version": 1
  }
}