Pith Number

pith:MYPZ6W57

pith:2010:MYPZ6W57EXXLTAZORYZ4H2IKQN

not attested not anchored not stored refs pending

Asymptotic invariants, complexity of groups and related problems

Mark Sapir

arxiv:1012.1325 v4 · 2010-12-06 · 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{MYPZ6W57EXXLTAZORYZ4H2IKQN}

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	2026-05-18T04:26:22.810985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

661f9f5bbf25eeb9832e8e33c3e90a837230ef39b272e2d3e3719c8cc1fc4fb0

Aliases

arxiv: 1012.1325 · arxiv_version: 1012.1325v4 · doi: 10.48550/arxiv.1012.1325 · pith_short_12: MYPZ6W57EXXL · pith_short_16: MYPZ6W57EXXLTAZO · pith_short_8: MYPZ6W57

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/MYPZ6W57EXXLTAZORYZ4H2IKQN \
  | 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: 661f9f5bbf25eeb9832e8e33c3e90a837230ef39b272e2d3e3719c8cc1fc4fb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e76912c0c03773de52b4cf6150ecb4e79afaaf1d91e7cc6a6f9ce3c7cdbbfd2",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-06T21:02:41Z",
    "title_canon_sha256": "265c7bacce822eab1d80b0a81e31cb8b906ae506452e90bd7aed8f9207b4582f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1325",
    "kind": "arxiv",
    "version": 4
  }
}