Pith Number

pith:RMJCFCAR

pith:2010:RMJCFCAR5FTEJV6LYWMMPEQMLD

not attested not anchored not stored refs pending

Geometric Auslander criterion for openness of an algebraic morphism

Edward Bierstone, Janusz Adamus, Pierre D. Milman

arxiv:1006.1872 v2 · 2010-06-09 · 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{RMJCFCAR5FTEJV6LYWMMPEQMLD}

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	2026-05-18T00:34:10.918105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b12228811e96644d7cbc598c7920c58eae7d83d09b1d61e74487dc2c410ae1d

Aliases

arxiv: 1006.1872 · arxiv_version: 1006.1872v2 · doi: 10.48550/arxiv.1006.1872 · pith_short_12: RMJCFCAR5FTE · pith_short_16: RMJCFCAR5FTEJV6L · pith_short_8: RMJCFCAR

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/RMJCFCAR5FTEJV6LYWMMPEQMLD \
  | 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: 8b12228811e96644d7cbc598c7920c58eae7d83d09b1d61e74487dc2c410ae1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5a1257221365223234bc64693a62d0be1223a95e3ac64356a0251298ab5bc04",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-06-09T18:40:46Z",
    "title_canon_sha256": "278698a0f953e96ebfab9e480695bc66bb8c9fec638d2a3e5a716a852677ae89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.1872",
    "kind": "arxiv",
    "version": 2
  }
}