Pith Number

pith:RATF4TM6

pith:2012:RATF4TM63MJPR42JAFZYOXWRRR

not attested not anchored not stored refs pending

On monoids of monotone injective partial self-maps of integers with cofinite domains and images

Du\v{s}an Repov\v{s}, Oleg Gutik

arxiv:1209.0587 v1 · 2012-09-04 · math.GR · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RATF4TM63MJPR42JAFZYOXWRRR}

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	2026-05-18T03:46:17.746506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88265e4d9edb12f8f3490173875ed18c41904f2df46ef122473cdcb5f18f234d

Aliases

arxiv: 1209.0587 · arxiv_version: 1209.0587v1 · doi: 10.48550/arxiv.1209.0587 · pith_short_12: RATF4TM63MJP · pith_short_16: RATF4TM63MJPR42J · pith_short_8: RATF4TM6

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/RATF4TM63MJPR42JAFZYOXWRRR \
  | 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: 88265e4d9edb12f8f3490173875ed18c41904f2df46ef122473cdcb5f18f234d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17b01cfa377ac85326bc63ffe84c08f3e29147ad10227eeb17cef77bfac6a5f3",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-09-04T10:08:50Z",
    "title_canon_sha256": "cb8243ca6acb2a47a0065db8ab5aa0758fda8d3fb896852ffa3474abcd481865"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0587",
    "kind": "arxiv",
    "version": 1
  }
}