Pith Number

pith:GRCPHW4Z

pith:2012:GRCPHW4ZWQ3SKUHW2NXEA2SQPZ

not attested not anchored not stored refs pending

Fixed points of nilpotent actions on ${\mathbb S}^{2}$

Javier Rib\'on

arxiv:1208.4510 v4 · 2012-08-22 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GRCPHW4ZWQ3SKUHW2NXEA2SQPZ}

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	2026-05-18T01:23:40.452072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3444f3db99b4372550f6d36e406a507e7ce22e14e67a89255a6a4154a4dc80d7

Aliases

arxiv: 1208.4510 · arxiv_version: 1208.4510v4 · doi: 10.48550/arxiv.1208.4510 · pith_short_12: GRCPHW4ZWQ3S · pith_short_16: GRCPHW4ZWQ3SKUHW · pith_short_8: GRCPHW4Z

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/GRCPHW4ZWQ3SKUHW2NXEA2SQPZ \
  | 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: 3444f3db99b4372550f6d36e406a507e7ce22e14e67a89255a6a4154a4dc80d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0165adbea9af2e95ad2b101f66d886deb994db325f7732c4e3b236a16ddc363c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-08-22T14:32:44Z",
    "title_canon_sha256": "cb5d87f3951c6d7d4432a0a26243387e7673a28b57d13f35409c00e109a7adda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4510",
    "kind": "arxiv",
    "version": 4
  }
}