Pith Number

pith:QUNDTVH4

pith:2012:QUNDTVH4CH2Y5LBNWKPELDUXQ3

not attested not anchored not stored refs pending

The boundary of the complex of free factors

Mladen Bestvina, Patrick Reynolds

arxiv:1211.3608 v2 · 2012-11-15 · 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{QUNDTVH4CH2Y5LBNWKPELDUXQ3}

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	2026-05-18T01:28:21.430834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

851a39d4fc11f58eac2db29e458e9786d587c9753933ce520f8889a163c61d64

Aliases

arxiv: 1211.3608 · arxiv_version: 1211.3608v2 · doi: 10.48550/arxiv.1211.3608 · pith_short_12: QUNDTVH4CH2Y · pith_short_16: QUNDTVH4CH2Y5LBN · pith_short_8: QUNDTVH4

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/QUNDTVH4CH2Y5LBNWKPELDUXQ3 \
  | 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: 851a39d4fc11f58eac2db29e458e9786d587c9753933ce520f8889a163c61d64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c9efb637a4df19292590602794a0e45197612767df93f46f99a1c22de5b1c00",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-15T14:00:00Z",
    "title_canon_sha256": "902c00bbdc072e580cd6a61e82b24aaf43d03a0d86a115d1b6876965a7584edf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3608",
    "kind": "arxiv",
    "version": 2
  }
}