Pith Number

pith:MYPGJMK6

pith:2015:MYPGJMK6624CZNCFCTBQDAMB4Z

not attested not anchored not stored refs pending

The complexity of balanced presentations and the Andrews-Curtis conjecture

Martin R. Bridson

arxiv:1504.04187 v1 · 2015-04-16 · 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{MYPGJMK6624CZNCFCTBQDAMB4Z}

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	2026-05-18T02:18:39.532382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

661e64b15ef6b82cb44514c3018181e679dde07706983284909e58727013c46e

Aliases

arxiv: 1504.04187 · arxiv_version: 1504.04187v1 · doi: 10.48550/arxiv.1504.04187 · pith_short_12: MYPGJMK6624C · pith_short_16: MYPGJMK6624CZNCF · pith_short_8: MYPGJMK6

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/MYPGJMK6624CZNCFCTBQDAMB4Z \
  | 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: 661e64b15ef6b82cb44514c3018181e679dde07706983284909e58727013c46e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bf4a3565fa061a87ece5a0c2cd2c5b99db4cef4ec464f0e1a1cf6ab66aee9d5",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-04-16T11:32:45Z",
    "title_canon_sha256": "e214a37bfa04ae739fb3633d9dafb21561da44b403c966e774e812cfa75f8bf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04187",
    "kind": "arxiv",
    "version": 1
  }
}