Pith Number

pith:CTGGYZY6

pith:2011:CTGGYZY6X4SCYQRGS5FDANOG7J

not attested not anchored not stored refs pending

An optimal gap theorem

Lei Ni

arxiv:1104.3185 v1 · 2011-04-16 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CTGGYZY6X4SCYQRGS5FDANOG7J}

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	2026-05-18T02:02:24.384086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14cc6c671ebf242c4226974a3035c6fa467f1acfb31ff544bbf0a666f7f378d7

Aliases

arxiv: 1104.3185 · arxiv_version: 1104.3185v1 · doi: 10.48550/arxiv.1104.3185 · pith_short_12: CTGGYZY6X4SC · pith_short_16: CTGGYZY6X4SCYQRG · pith_short_8: CTGGYZY6

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/CTGGYZY6X4SCYQRGS5FDANOG7J \
  | 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: 14cc6c671ebf242c4226974a3035c6fa467f1acfb31ff544bbf0a666f7f378d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2450a7ad67e5663228e7fe2446f0dda1026aba74a3940fcf1978a6d09c2b6aa",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-04-16T01:54:35Z",
    "title_canon_sha256": "9f4d65adf9fe4959a84df9f4d2b268ea64a98bbb0ec7876ad62d5664d88076e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3185",
    "kind": "arxiv",
    "version": 1
  }
}