Pith Number

pith:CMSZBPWR

pith:2016:CMSZBPWR7JAAQG3DAXQ7SK5YOM

not attested not anchored not stored refs pending

On joins and intersections of subgroups in free groups

Sergei V. Ivanov

arxiv:1607.04890 v1 · 2016-07-17 · 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{CMSZBPWR7JAAQG3DAXQ7SK5YOM}

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	2026-05-18T01:10:56.428617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

132590bed1fa40081b6305e1f92bb873171714a1b2f16ca7f378b470866e19bc

Aliases

arxiv: 1607.04890 · arxiv_version: 1607.04890v1 · doi: 10.48550/arxiv.1607.04890 · pith_short_12: CMSZBPWR7JAA · pith_short_16: CMSZBPWR7JAAQG3D · pith_short_8: CMSZBPWR

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/CMSZBPWR7JAAQG3DAXQ7SK5YOM \
  | 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: 132590bed1fa40081b6305e1f92bb873171714a1b2f16ca7f378b470866e19bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a47eca1a34a6d4c3f9b4a920a7937570bb5af83b3f4859a2dce250a4817aa9dc",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-17T16:20:59Z",
    "title_canon_sha256": "75fa41dcabea47b5f3db59951a27ee81b1456f6db4137358517c5670dc575a1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.04890",
    "kind": "arxiv",
    "version": 1
  }
}