Pith Number

pith:2JUUH7H6

pith:2014:2JUUH7H6VFFKC2JMPHBLVDLNRW

not attested not anchored not stored refs pending

Mapping tori of free group automorphisms, and the Bieri-Neumann-Strebel invariant of graphs of groups

Christopher H. Cashen, Gilbert Levitt

arxiv:1412.8582 v1 · 2014-12-30 · 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{2JUUH7H6VFFKC2JMPHBLVDLNRW}

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	2026-05-18T01:12:01.886070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d26943fcfea94aa1692c79c2ba8d6d8da3be493efb016aa923e89f83c30adc14

Aliases

arxiv: 1412.8582 · arxiv_version: 1412.8582v1 · doi: 10.48550/arxiv.1412.8582 · pith_short_12: 2JUUH7H6VFFK · pith_short_16: 2JUUH7H6VFFKC2JM · pith_short_8: 2JUUH7H6

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/2JUUH7H6VFFKC2JMPHBLVDLNRW \
  | 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: d26943fcfea94aa1692c79c2ba8d6d8da3be493efb016aa923e89f83c30adc14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06dece62f3cb30b6383b909bb725934875e9db0098785f563932f217c81fc92e",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-12-30T08:45:21Z",
    "title_canon_sha256": "04c44aa18d31f3afd42d12666713fd71a9c68038b02c36977aa92f4cf923d54f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8582",
    "kind": "arxiv",
    "version": 1
  }
}