Pith Number

pith:HX7DOPVY

pith:1994:HX7DOPVY5XMVLCBYCQJD24XKLZ

not attested not anchored not stored refs pending

Invertible families of sets of bounded degree

Emanuel Knill

arxiv:math/9409214 v1 · 1994-09-16 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HX7DOPVY5XMVLCBYCQJD24XKLZ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:05:51.103373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dfe373eb8edd955883814123d72ea5e46c6de23e2effaa57276d9db9868d073

Aliases

arxiv: math/9409214 · arxiv_version: math/9409214v1 · doi: 10.48550/arxiv.math/9409214 · pith_short_12: HX7DOPVY5XMV · pith_short_16: HX7DOPVY5XMVLCBY · pith_short_8: HX7DOPVY

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/HX7DOPVY5XMVLCBYCQJD24XKLZ \
  | 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: 3dfe373eb8edd955883814123d72ea5e46c6de23e2effaa57276d9db9868d073

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "382e4e97c38a470728bface3d63655f89b1318dca43e7d6a4e40bb4e693faff7",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1994-09-16T00:00:00Z",
    "title_canon_sha256": "cdc907f23ccdd4e54cb9fe6e0819718d6d15a44ab337ec56a622a76fedc79e46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9409214",
    "kind": "arxiv",
    "version": 1
  }
}