Pith Number

pith:RNUCUY5N

pith:2009:RNUCUY5NQQMO5YLDUAXI5FX6TM

not attested not anchored not stored refs pending

On Additive invariants of actions of additive and multiplicative groups

Wenchuan Hu

arxiv:0912.0563 v2 · 2009-12-03 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RNUCUY5NQQMO5YLDUAXI5FX6TM}

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	2026-05-18T04:38:48.573170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b682a63ad8418eee163a02e8e96fe9b02e3d807b4488ae3e77d689b197e8014

Aliases

arxiv: 0912.0563 · arxiv_version: 0912.0563v2 · doi: 10.48550/arxiv.0912.0563 · pith_short_12: RNUCUY5NQQMO · pith_short_16: RNUCUY5NQQMO5YLD · pith_short_8: RNUCUY5N

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/RNUCUY5NQQMO5YLDUAXI5FX6TM \
  | 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: 8b682a63ad8418eee163a02e8e96fe9b02e3d807b4488ae3e77d689b197e8014

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff18af58089f69c6d11994794b3ba502a3a2251eb53398bdffd81b92507bb2c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-12-03T01:30:18Z",
    "title_canon_sha256": "946c707c497d17563c1553ba5c6321596f36ac4b6e78525ab96d5df2f5a4bc66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0563",
    "kind": "arxiv",
    "version": 2
  }
}