Pith Number

pith:QGXE7JIJ

pith:2016:QGXE7JIJXJWZC2T6Q62NPOBPRI

not attested not anchored not stored refs pending

Numerical evidence for a phase transition in 4d spin foam quantum gravity

Benjamin Bahr, Sebastian Steinhaus

arxiv:1605.07649 v2 · 2016-05-24 · 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{QGXE7JIJXJWZC2T6Q62NPOBPRI}

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	2026-05-18T01:02:30.570031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81ae4fa509ba6d916a7e87b4d7b82f8a335235673892520b7080c08614ad4083

Aliases

arxiv: 1605.07649 · arxiv_version: 1605.07649v2 · doi: 10.48550/arxiv.1605.07649 · pith_short_12: QGXE7JIJXJWZ · pith_short_16: QGXE7JIJXJWZC2T6 · pith_short_8: QGXE7JIJ

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/QGXE7JIJXJWZC2T6Q62NPOBPRI \
  | 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: 81ae4fa509ba6d916a7e87b4d7b82f8a335235673892520b7080c08614ad4083

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d3c1a2d4c7da237962cd6cdf8b4a7dc26717f45f6e877d206d7363879910377",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-05-24T20:30:14Z",
    "title_canon_sha256": "8fccc7c680a9c1e2b2ebaeaaf3421df51b66622eb432ebb4934c8b6c773a4190"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.07649",
    "kind": "arxiv",
    "version": 2
  }
}