Pith Number

pith:W2W636PP

pith:1999:W2W636PPJ4OFSINTQO6OTMQ4TM

not attested not anchored not stored refs pending

Critical Phenomena in Nonlinear Sigma Models

Eric W. Hirschmann, James Isenberg, Steven L. Liebling

arxiv:math-ph/9911020 v2 · 1999-11-13 · math-ph · gr-qc · hep-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W2W636PPJ4OFSINTQO6OTMQ4TM}

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	2026-05-18T01:38:30.439130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6adedf9ef4f1c5921b383bce9b21c9b385ed699717e959e6e73aae52eba421d

Aliases

arxiv: math-ph/9911020 · arxiv_version: math-ph/9911020v2 · doi: 10.48550/arxiv.math-ph/9911020 · pith_short_12: W2W636PPJ4OF · pith_short_16: W2W636PPJ4OFSINT · pith_short_8: W2W636PP

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/W2W636PPJ4OFSINTQO6OTMQ4TM \
  | 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: b6adedf9ef4f1c5921b383bce9b21c9b385ed699717e959e6e73aae52eba421d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc62f6a7ec444597624fe444528af9eff10156798312c2fbda6fd22935a48193",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "1999-11-13T18:09:50Z",
    "title_canon_sha256": "33ea1ba5c6d47f4f9b12508b53f113e68fd5fdff67b43706ebf558f2eabf48a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/9911020",
    "kind": "arxiv",
    "version": 2
  }
}