Pith Number

pith:NGBWFVUT

pith:2015:NGBWFVUTB4SX2Y4NTXWBZXMAZE

not attested not anchored not stored refs pending

Relaxations of associativity and preassociativity for variadic functions

Bruno Teheux, Jean-Luc Marichal, Miguel Couceiro

arxiv:1508.03310 v1 · 2015-08-13 · math.GR · cs.DM · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NGBWFVUTB4SX2Y4NTXWBZXMAZE}

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	2026-05-18T01:12:18.345710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

698362d6930f257d638d9dec1cdd80c93263318aba973868300217102192ee2f

Aliases

arxiv: 1508.03310 · arxiv_version: 1508.03310v1 · doi: 10.48550/arxiv.1508.03310 · pith_short_12: NGBWFVUTB4SX · pith_short_16: NGBWFVUTB4SX2Y4N · pith_short_8: NGBWFVUT

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/NGBWFVUTB4SX2Y4NTXWBZXMAZE \
  | 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: 698362d6930f257d638d9dec1cdd80c93263318aba973868300217102192ee2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bcfab48cf3aa5196ee10c9571fbaab70a250d917036e9e2ee2c2fba7db42943",
    "cross_cats_sorted": [
      "cs.DM",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-08-13T19:11:11Z",
    "title_canon_sha256": "9749f89824f0c42034c370790df7b2cdace6263ea3eabdf7d49d7db2325e623a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03310",
    "kind": "arxiv",
    "version": 1
  }
}