Pith Number

pith:XDK725NH

pith:2017:XDK725NHZWLZDELK2AFKVMVXAW

not attested not anchored not stored refs pending

The Nonassociativity of the Double Minus Operation

Jia Huang, Jianbai Xu, Madison Mickey

arxiv:1710.05651 v1 · 2017-10-16 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XDK725NHZWLZDELK2AFKVMVXAW}

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	2026-05-18T00:32:48.655360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8d5fd75a7cd9791916ad00aaab2b705a02162c259d19fec1dba451a016d8567

Aliases

arxiv: 1710.05651 · arxiv_version: 1710.05651v1 · doi: 10.48550/arxiv.1710.05651 · pith_short_12: XDK725NHZWLZ · pith_short_16: XDK725NHZWLZDELK · pith_short_8: XDK725NH

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/XDK725NHZWLZDELK2AFKVMVXAW \
  | 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: b8d5fd75a7cd9791916ad00aaab2b705a02162c259d19fec1dba451a016d8567

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70c07eaef5494cfb0076c09fcf5eba8135b6cc9f92b3f581eb38eac525e9aa8a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-10-16T12:34:25Z",
    "title_canon_sha256": "0d9d08c9b349a0db86d3d0082b4edde5b52b43e497d70af8ebe25bafd4f97b80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.05651",
    "kind": "arxiv",
    "version": 1
  }
}