Pith Number

pith:2CIQF26C

pith:2012:2CIQF26C6QE4NIVUASDC76RRU2

not attested not anchored not stored refs pending

Lower central series of a free associative algebra over the integers and finite fields

David Jordan, Jason Li, Pavel Etingof, Surya Bhupatiraju, William Kuszmaul

arxiv:1203.1893 v1 · 2012-03-08 · math.RA · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2CIQF26C6QE4NIVUASDC76RRU2}

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	2026-05-18T01:03:37.334565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d09102ebc2f409c6a2b404862ffa31a695fd2c63ae0e3459694077f12601cb1e

Aliases

arxiv: 1203.1893 · arxiv_version: 1203.1893v1 · doi: 10.48550/arxiv.1203.1893 · pith_short_12: 2CIQF26C6QE4 · pith_short_16: 2CIQF26C6QE4NIVU · pith_short_8: 2CIQF26C

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/2CIQF26C6QE4NIVUASDC76RRU2 \
  | 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: d09102ebc2f409c6a2b404862ffa31a695fd2c63ae0e3459694077f12601cb1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9a063a7b99a0e83db59524fee41caa2922cd87dceeaffe54cf8bc6fda79145d",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-03-08T19:25:14Z",
    "title_canon_sha256": "97154178c11a35d0226ac67a101a4056613641a192f6f600f494c1e6ba096b19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1893",
    "kind": "arxiv",
    "version": 1
  }
}