Pith Number

pith:WQ7XB3HK

pith:2013:WQ7XB3HKVINC6EPA7VQ25KSGVB

not attested not anchored not stored refs pending

Powers of the Phantom Ideal

Ivo Herzog, Xianhui Fu

arxiv:1312.5348 v1 · 2013-12-18 · math.CT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WQ7XB3HKVINC6EPA7VQ25KSGVB}

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	2026-05-18T00:44:29.244828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b43f70eceaaa1a2f11e0fd61aeaa46a86da96d20fff90ff9a8a0ac86275432a7

Aliases

arxiv: 1312.5348 · arxiv_version: 1312.5348v1 · doi: 10.48550/arxiv.1312.5348 · pith_short_12: WQ7XB3HKVINC · pith_short_16: WQ7XB3HKVINC6EPA · pith_short_8: WQ7XB3HK

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/WQ7XB3HKVINC6EPA7VQ25KSGVB \
  | 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: b43f70eceaaa1a2f11e0fd61aeaa46a86da96d20fff90ff9a8a0ac86275432a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60dac1f5b4cad7c3e7e24401c3244ebb355436deaed7ef426d86bcd603b66b96",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2013-12-18T21:38:42Z",
    "title_canon_sha256": "e6b52cb038a483531723976e45ab5576007af15f3dfbc4b86d0ffe0bcbabe076"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5348",
    "kind": "arxiv",
    "version": 1
  }
}