Pith Number

pith:V7WWUMM5

pith:2026:V7WWUMM5WE5YHOVVVZIMHP4NIE

not attested not anchored not stored refs pending

The stable Andrews-Curtis conjecture and thickenable presentations of the trivial group

Marc Lackenby

arxiv:2606.06122 v1 · 2026-06-04 · 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{V7WWUMM5WE5YHOVVVZIMHP4NIE}

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	2026-06-05T01:15:34.121752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afed6a319db13b83bab5ae50c3bf8d41001e0e63f6e77892a4b3ad588e9abcbb

Aliases

arxiv: 2606.06122 · arxiv_version: 2606.06122v1 · doi: 10.48550/arxiv.2606.06122 · pith_short_12: V7WWUMM5WE5Y · pith_short_16: V7WWUMM5WE5YHOVV · pith_short_8: V7WWUMM5

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/V7WWUMM5WE5YHOVVVZIMHP4NIE \
  | 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: afed6a319db13b83bab5ae50c3bf8d41001e0e63f6e77892a4b3ad588e9abcbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ff6d5ea4d01975b1d3a24785f16d777d681f79adbff8d6c59d14bb0a3f3450d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-06-04T13:09:26Z",
    "title_canon_sha256": "6a1624f8c1325cdcd606642759033d2bf72b5e7bd9af736b20ceed539b37f1ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06122",
    "kind": "arxiv",
    "version": 1
  }
}