Pith Number

pith:IIYTHY2Z

pith:2015:IIYTHY2ZIIXD2RCQLVJTWTDLHZ

not attested not anchored not stored refs pending

Ideal Whitehead Graphs in $Out(F_r)$ IV: Building ideal Whitehead graphs in higher ranks and ideal Whitehead graphs with cut vertices

Catherine Pfaff

arxiv:1511.08933 v1 · 2015-11-28 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IIYTHY2ZIIXD2RCQLVJTWTDLHZ}

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	2026-05-18T01:25:46.067312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

423133e359422e3d44505d533b4c6b3e5c73292db0d5173fa98b1ca796c5d512

Aliases

arxiv: 1511.08933 · arxiv_version: 1511.08933v1 · doi: 10.48550/arxiv.1511.08933 · pith_short_12: IIYTHY2ZIIXD · pith_short_16: IIYTHY2ZIIXD2RCQ · pith_short_8: IIYTHY2Z

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/IIYTHY2ZIIXD2RCQLVJTWTDLHZ \
  | 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: 423133e359422e3d44505d533b4c6b3e5c73292db0d5173fa98b1ca796c5d512

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb5a149d6fd31c72a4408e9b2f786ac4210fb5a9c528c760a2baa25b7e291789",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-11-28T21:31:38Z",
    "title_canon_sha256": "7baab2eea4c720a383a4e64fea5042f653b8f210e41cfdcf14e1ab23c31c337c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08933",
    "kind": "arxiv",
    "version": 1
  }
}