Pith Number

pith:QAFYEG3I

pith:2026:QAFYEG3IA3G3DSR6V7BF3W6BPK

not attested not anchored not stored refs pending

Adjoining Idempotents to a Commutative Ring preprint version

R. Raphael, W.D. Burgess

arxiv:2606.21782 v1 · 2026-06-19 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QAFYEG3IA3G3DSR6V7BF3W6BPK}

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	2026-06-23T01:13:22.500867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

800b821b6806cdb1ca3eafc25ddbc17aa0dffb8424de010ae1fe6b695f7fdf16

Aliases

arxiv: 2606.21782 · arxiv_version: 2606.21782v1 · doi: 10.48550/arxiv.2606.21782 · pith_short_12: QAFYEG3IA3G3 · pith_short_16: QAFYEG3IA3G3DSR6 · pith_short_8: QAFYEG3I

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/QAFYEG3IA3G3DSR6V7BF3W6BPK \
  | 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: 800b821b6806cdb1ca3eafc25ddbc17aa0dffb8424de010ae1fe6b695f7fdf16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c60ad65436986dc3691100d031ef76c58980680345fd36dd8e551b4e15223386",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-06-19T22:05:04Z",
    "title_canon_sha256": "c3712aacd1372c8864a44667bcb502bb4c7780a67e85c2a52011276c63e04d92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21782",
    "kind": "arxiv",
    "version": 1
  }
}