Pith Number

pith:CR2NROPN

pith:2019:CR2NROPNCFTMLSGKOT7LUONKSN

not attested not anchored not stored refs pending

Twisted associativity of the cyclically reduced product of words, part 1

Carmelo Vaccaro

arxiv:1909.04863 v4 · 2019-09-11 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CR2NROPNCFTMLSGKOT7LUONKSN}

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.

Cited by

1 paper in Pith

An Analytic Threshold for LESA-Driven Negative ELN Flux Directions in Core-Collapse Supernovae: Derivation and Population Census

Receipt and verification

First computed	2026-07-05T03:44:05.848631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1474d8b9ed1166c5c8ca74feba39aa9373b3b2e20ce78eae3b29bc47051192e1

Aliases

arxiv: 1909.04863 · arxiv_version: 1909.04863v4 · doi: 10.48550/arxiv.1909.04863 · pith_short_12: CR2NROPNCFTM · pith_short_16: CR2NROPNCFTMLSGK · pith_short_8: CR2NROPN

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/CR2NROPNCFTMLSGKOT7LUONKSN \
  | 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: 1474d8b9ed1166c5c8ca74feba39aa9373b3b2e20ce78eae3b29bc47051192e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2e8b4e9ddbe6058e396fbc7a24d5b010f1cc4a9154a9c04c4b7ef08e458c865",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-09-11T05:57:43Z",
    "title_canon_sha256": "25912251aea0d1fcb2a389cdabae4fdc214d1f88b6d073d24c9badb302dd0eda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.04863",
    "kind": "arxiv",
    "version": 4
  }
}