Pith Number

pith:KBR5MNUQ

pith:2013:KBR5MNUQ7CDZPS4OQH6M25GIGF

not attested not anchored not stored refs pending

Explicit left orders on free groups extending the lexicographic order on free monoids

Zoran Sunic

arxiv:1304.0837 v1 · 2013-04-03 · 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{KBR5MNUQ7CDZPS4OQH6M25GIGF}

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	2026-05-18T03:29:05.995907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5063d63690f88797cb8e81fccd74c831410fb7ed522e0fdd0bbaa4053f421b51

Aliases

arxiv: 1304.0837 · arxiv_version: 1304.0837v1 · doi: 10.48550/arxiv.1304.0837 · pith_short_12: KBR5MNUQ7CDZ · pith_short_16: KBR5MNUQ7CDZPS4O · pith_short_8: KBR5MNUQ

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/KBR5MNUQ7CDZPS4OQH6M25GIGF \
  | 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: 5063d63690f88797cb8e81fccd74c831410fb7ed522e0fdd0bbaa4053f421b51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70b3937e0269bd107177d34ad8707cb7836d0cb81f1610aedd2f9df26d8125f0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-04-03T03:57:22Z",
    "title_canon_sha256": "08ff4b5f3e83676440ec54559b31e3701d075cd34ea5ea2a484419dae210c548"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0837",
    "kind": "arxiv",
    "version": 1
  }
}