Pith Number

pith:DJY5NYCP

pith:2026:DJY5NYCPRAZSAHMBI6IBFUBHQZ

not attested not anchored not stored refs pending

Modified Cosmology from Mass-to-Horizon Relation: Observational Bounds

Hussain Gohar, Pranav Prasanthan, Vincenzo Salzano

arxiv:2607.18521 v1 · 2026-07-20 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DJY5NYCPRAZSAHMBI6IBFUBHQZ}

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	2026-07-22T00:22:52.620433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a71d6e04f8833201d81479012d0278671f1d05a7dbce8ae9401a3cc7eac8972

Aliases

arxiv: 2607.18521 · arxiv_version: 2607.18521v1 · doi: 10.48550/arxiv.2607.18521 · pith_short_12: DJY5NYCPRAZS · pith_short_16: DJY5NYCPRAZSAHMB · pith_short_8: DJY5NYCP

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/DJY5NYCPRAZSAHMBI6IBFUBHQZ \
  | 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: 1a71d6e04f8833201d81479012d0278671f1d05a7dbce8ae9401a3cc7eac8972

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7178ade92c8d712f9f3e57d44ce2f312d65f08857d42a2cde4a202ebef879f3",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-20T21:33:34Z",
    "title_canon_sha256": "629e857ee8095c30884eac3032a15b5474a0899699bd7a0536873529fec4f986"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.18521",
    "kind": "arxiv",
    "version": 1
  }
}