Pith Number

pith:GGBCE4ZN

pith:2012:GGBCE4ZNEGYOR7PJU5L7UZ2GCI

not attested not anchored not stored refs pending

A note on the rank of positive closed currents

Romain Dujardin

arxiv:1203.5821 v1 · 2012-03-26 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GGBCE4ZNEGYOR7PJU5L7UZ2GCI}

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	2026-05-18T03:59:13.355029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

318222732d21b0e8fde9a757fa6746123fc101cbcd2381e6e0e96dee0f0b14f6

Aliases

arxiv: 1203.5821 · arxiv_version: 1203.5821v1 · doi: 10.48550/arxiv.1203.5821 · pith_short_12: GGBCE4ZNEGYO · pith_short_16: GGBCE4ZNEGYOR7PJ · pith_short_8: GGBCE4ZN

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/GGBCE4ZNEGYOR7PJU5L7UZ2GCI \
  | 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: 318222732d21b0e8fde9a757fa6746123fc101cbcd2381e6e0e96dee0f0b14f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6aae995ea15e81094fd8c2922d0107e0da07493287917cece3262815e33d58c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2012-03-26T21:18:06Z",
    "title_canon_sha256": "ebf8e2a0f86b1150eafad08014ee0c4229879c751cf0554c93ff7cdbe00908a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5821",
    "kind": "arxiv",
    "version": 1
  }
}