Pith Number

pith:YJLXNKU4

pith:2014:YJLXNKU4H5HHJXEM524MOAUAQY

not attested not anchored not stored refs pending

A combination theorem for cubulation in small cancellation theory over free products

Alexandre Martin, Markus Steenbock

arxiv:1409.3678 v2 · 2014-09-12 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YJLXNKU4H5HHJXEM524MOAUAQY}

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	2026-05-18T01:23:50.889337Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c25776aa9c3f4e74dc8ceeb8c70280860adb3805ef6d0a007972261b7e040e2b

Aliases

arxiv: 1409.3678 · arxiv_version: 1409.3678v2 · doi: 10.48550/arxiv.1409.3678 · pith_short_12: YJLXNKU4H5HH · pith_short_16: YJLXNKU4H5HHJXEM · pith_short_8: YJLXNKU4

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/YJLXNKU4H5HHJXEM524MOAUAQY \
  | 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: c25776aa9c3f4e74dc8ceeb8c70280860adb3805ef6d0a007972261b7e040e2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6ece1e553104e1846d30b4aa988b5ebe0afd249f715cd799d11c1583dc0d0e1",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-09-12T08:39:21Z",
    "title_canon_sha256": "e790a19badcace999aa34ebe0593def165edad3737c1a3829610a82259ebef4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.3678",
    "kind": "arxiv",
    "version": 2
  }
}