Pith Number

pith:UKCUO5VA

pith:2026:UKCUO5VAZB4JFJWQXZ5GC2ZWPL

not attested not anchored not stored refs pending

Saturation Equations of State in Critical Gravitational Collapse: The Primordial Black Hole Threshold

Benaoumeur Bakhti

arxiv:2606.29590 v1 · 2026-06-28 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UKCUO5VAZB4JFJWQXZ5GC2ZWPL}

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	2026-06-30T01:18:13.287640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2854776a0c87892a6d0be7a616b367ad4de91db01905de7c38f8dd02acab62e

Aliases

arxiv: 2606.29590 · arxiv_version: 2606.29590v1 · doi: 10.48550/arxiv.2606.29590 · pith_short_12: UKCUO5VAZB4J · pith_short_16: UKCUO5VAZB4JFJWQ · pith_short_8: UKCUO5VA

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/UKCUO5VAZB4JFJWQXZ5GC2ZWPL \
  | 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: a2854776a0c87892a6d0be7a616b367ad4de91db01905de7c38f8dd02acab62e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2e9025750ac84a6f840616c34a825a65451050eaa8a4ae774839fd1ea06ab32",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-06-28T20:21:27Z",
    "title_canon_sha256": "8dfd856a4b74cf9f8c0029833909d4464b7821728b87f76c23389f9b07877dfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29590",
    "kind": "arxiv",
    "version": 1
  }
}