Pith Number

pith:CKF2BIMX

pith:2018:CKF2BIMX2SIIRG36SVNVWXVLUQ

not attested not anchored not stored refs pending

Quasi-positivity and recognition of products of conjugacy classes in free groups

Rita Gitik, Robert W. Bell

arxiv:1808.03291 v3 · 2018-08-09 · 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{CKF2BIMX2SIIRG36SVNVWXVLUQ}

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	2026-05-17T23:55:20.149199Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

128ba0a197d490889b7e955b5b5eaba402885cd81bb187f91c1ca5afda6f69f4

Aliases

arxiv: 1808.03291 · arxiv_version: 1808.03291v3 · doi: 10.48550/arxiv.1808.03291 · pith_short_12: CKF2BIMX2SII · pith_short_16: CKF2BIMX2SIIRG36 · pith_short_8: CKF2BIMX

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/CKF2BIMX2SIIRG36SVNVWXVLUQ \
  | 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: 128ba0a197d490889b7e955b5b5eaba402885cd81bb187f91c1ca5afda6f69f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7df8418ff4a4938c695e168e29389e32c665f2aaf180cb5d1205ab9f2f9f7dd6",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-08-09T18:13:38Z",
    "title_canon_sha256": "1da9b57c8c1517f909827aba2514f9e7891f7088a7b4733f946f06914cfa4351"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.03291",
    "kind": "arxiv",
    "version": 3
  }
}