Pith Number

pith:D2Z2LOWB

pith:2012:D2Z2LOWBASCCZ7FS3TJHLGWPXJ

not attested not anchored not stored refs pending

An integral weight realization theorem for subset currents on free groups

Ilya Kapovich

arxiv:1211.5836 v4 · 2012-11-26 · 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{D2Z2LOWBASCCZ7FS3TJHLGWPXJ}

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	2026-05-18T00:55:39.709357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1eb3a5bac104842cfcb2dcd2759acfba6b9969d655b282e815e9959298566131

Aliases

arxiv: 1211.5836 · arxiv_version: 1211.5836v4 · doi: 10.48550/arxiv.1211.5836 · pith_short_12: D2Z2LOWBASCC · pith_short_16: D2Z2LOWBASCCZ7FS · pith_short_8: D2Z2LOWB

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/D2Z2LOWBASCCZ7FS3TJHLGWPXJ \
  | 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: 1eb3a5bac104842cfcb2dcd2759acfba6b9969d655b282e815e9959298566131

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97c40f1df2f4eb3aa8697c73cb992a81fd851a5e576d72bd864736036279deca",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-26T01:33:27Z",
    "title_canon_sha256": "ad3b0aa14b4955e90341f1c413baf0337608e2889cbecb56677f5cb93d3bb15d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5836",
    "kind": "arxiv",
    "version": 4
  }
}