Pith Number

pith:VBJPHCR5

pith:2014:VBJPHCR5ZYV2G3F54YYMI72TH7

not attested not anchored not stored refs pending

Relative free splitting and free factor complexes I: Hyperbolicity

Lee Mosher, Michael Handel

arxiv:1407.3508 v3 · 2014-07-13 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VBJPHCR5ZYV2G3F54YYMI72TH7}

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

Bond thickenings of the simplicial boundary of Outer space

Receipt and verification

First computed	2026-07-05T10:28:08.281518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a852f38a3dce2ba36cbde630c47f533fe61b3607a64ceb172542b02f3769239a

Aliases

arxiv: 1407.3508 · arxiv_version: 1407.3508v3 · doi: 10.48550/arxiv.1407.3508 · pith_short_12: VBJPHCR5ZYV2 · pith_short_16: VBJPHCR5ZYV2G3F5 · pith_short_8: VBJPHCR5

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/VBJPHCR5ZYV2G3F54YYMI72TH7 \
  | 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: a852f38a3dce2ba36cbde630c47f533fe61b3607a64ceb172542b02f3769239a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "784fa65ae69671b7832927ea177cc7e386bd23db5b32071ecf3735479c09617b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-07-13T22:19:33Z",
    "title_canon_sha256": "45a28a9e79665ca2ff192a0dd6a4da84bf0b36e6f7b78c82377858de32230647"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.3508",
    "kind": "arxiv",
    "version": 3
  }
}