Pith Number

pith:HBPQFIML

pith:1993:HBPQFIMLT6WRIQNKUBAQ4K7GZF

not attested not anchored not stored refs pending

Computational aspects of the gravitational instability problem for a multicomponent cosmological medium

Arak Mathai Mathai, Hans J. Haubold

arxiv:math/9307214 v1 · 1993-07-09 · math.CA · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HBPQFIMLT6WRIQNKUBAQ4K7GZF}

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	2026-05-18T01:05:52.069793Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

385f02a18b9fad1441aaa0410e2be6c94592d147ce55887cbb9e415c72f70867

Aliases

arxiv: math/9307214 · arxiv_version: math/9307214v1 · doi: 10.48550/arxiv.math/9307214 · pith_short_12: HBPQFIMLT6WR · pith_short_16: HBPQFIMLT6WRIQNK · pith_short_8: HBPQFIML

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/HBPQFIMLT6WRIQNKUBAQ4K7GZF \
  | 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: 385f02a18b9fad1441aaa0410e2be6c94592d147ce55887cbb9e415c72f70867

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb95dfa549ae464cd5694f28368b8040b3839d485011ed5f56aaf56767b7563f",
    "cross_cats_sorted": [
      "astro-ph"
    ],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "1993-07-09T00:00:00Z",
    "title_canon_sha256": "80efcb7c83724b657a1f341eaa8e73d8e8e8962feb8c91a1211f201e14d55007"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9307214",
    "kind": "arxiv",
    "version": 1
  }
}