Pith Number

pith:AYWECOU5

pith:1998:AYWECOU5BPISHK6PB7EHO7VVX7

not attested not anchored not stored refs pending

String Expansion as 't Hooft's Expansion

Zurab Kakushadze

arxiv:hep-th/9808019 v1 · 1998-08-05 · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AYWECOU5BPISHK6PB7EHO7VVX7}

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	2026-05-18T02:52:24.006720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

062c413a9d0bd123abcf0fc8777eb5bff201604809b8861ca82fab798bee8191

Aliases

arxiv: hep-th/9808019 · arxiv_version: hep-th/9808019v1 · doi: 10.48550/arxiv.hep-th/9808019 · pith_short_12: AYWECOU5BPIS · pith_short_16: AYWECOU5BPISHK6P · pith_short_8: AYWECOU5

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/AYWECOU5BPISHK6PB7EHO7VVX7 \
  | 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: 062c413a9d0bd123abcf0fc8777eb5bff201604809b8861ca82fab798bee8191

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7506a929b93336cc19dc28e3908fa275cb4f3f172a034ee7559bb7b880f2343",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "1998-08-05T05:56:31Z",
    "title_canon_sha256": "2824272d13508a39f09fe1d3ee862049a4bf77952b622cafc2c81626a35e810d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/9808019",
    "kind": "arxiv",
    "version": 1
  }
}