Pith Number

pith:3HR3DEAM

pith:2010:3HR3DEAMCP5HIQNN74IHH2RWXT

not attested not anchored not stored refs pending

Proof of the fundamental gap conjecture

Ben Andrews, Julie Clutterbuck

arxiv:1006.1686 v2 · 2010-06-09 · math.SP · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3HR3DEAMCP5HIQNN74IHH2RWXT}

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	2026-05-18T04:31:51.107254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9e3b1900c13fa7441adff1073ea36bcf79a19f62b3450ae8e93301c4293a27e

Aliases

arxiv: 1006.1686 · arxiv_version: 1006.1686v2 · doi: 10.48550/arxiv.1006.1686 · pith_short_12: 3HR3DEAMCP5H · pith_short_16: 3HR3DEAMCP5HIQNN · pith_short_8: 3HR3DEAM

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/3HR3DEAMCP5HIQNN74IHH2RWXT \
  | 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: d9e3b1900c13fa7441adff1073ea36bcf79a19f62b3450ae8e93301c4293a27e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "810d7c9847be8ee317123e4f045d95e5f39e26f7a88e798c5516c9e3aea834aa",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-06-09T02:26:32Z",
    "title_canon_sha256": "e23e05142deba9a2348e5d9774586e954a86e95914f3f82ac6c8f813f6e32656"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.1686",
    "kind": "arxiv",
    "version": 2
  }
}