Pith Number

pith:AZH3EROC

pith:2018:AZH3EROCHFFDAVQAPL3ZYRHBMA

not attested not anchored not stored refs pending

Homotopy type of the complex of free factors of a free group

Benjamin Br\"uck, Radhika Gupta

arxiv:1810.09380 v3 · 2018-10-22 · 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{AZH3EROCHFFDAVQAPL3ZYRHBMA}

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.

Cited by

1 paper in Pith

The minimally displaced set of an irreducible automorphism is locally finite

Receipt and verification

First computed	2026-07-05T01:32:40.521096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

064fb245c2394a3056007af79c44e16009e7b11ac4ed633c2534f4cb689fb30c

Aliases

arxiv: 1810.09380 · arxiv_version: 1810.09380v3 · doi: 10.48550/arxiv.1810.09380 · pith_short_12: AZH3EROCHFFD · pith_short_16: AZH3EROCHFFDAVQA · pith_short_8: AZH3EROC

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/AZH3EROCHFFDAVQAPL3ZYRHBMA \
  | 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: 064fb245c2394a3056007af79c44e16009e7b11ac4ed633c2534f4cb689fb30c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5227bf7c0cf0e56393f815afc5e5e95409273151329143a4bfc62c83199b608",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-10-22T16:00:43Z",
    "title_canon_sha256": "79c568d76de3dcf0a589b38a54d0c2624e31313dfa7a8a6a84e86d104a3f93a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.09380",
    "kind": "arxiv",
    "version": 3
  }
}