Pith Number

pith:23DV6HJ7

pith:2012:23DV6HJ7DJQRWFXHHGPNIRSTPB

not attested not anchored not stored refs pending

Mountain Pass Theorem With infinite symmetry

Noe Barcenas

arxiv:1208.0766 v3 · 2012-08-03 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{23DV6HJ7DJQRWFXHHGPNIRSTPB}

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	2026-05-18T02:42:29.210891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6c75f1d3f1a611b16e7399ed44653784def3a33da3f435f7ae81cfb8720b5c0

Aliases

arxiv: 1208.0766 · arxiv_version: 1208.0766v3 · doi: 10.48550/arxiv.1208.0766 · pith_short_12: 23DV6HJ7DJQR · pith_short_16: 23DV6HJ7DJQRWFXH · pith_short_8: 23DV6HJ7

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/23DV6HJ7DJQRWFXHHGPNIRSTPB \
  | 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: d6c75f1d3f1a611b16e7399ed44653784def3a33da3f435f7ae81cfb8720b5c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c643f86ee9b9beebb5549c1802b0299427017f2900efba27d1de34a1065cc25a",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-08-03T14:57:50Z",
    "title_canon_sha256": "0f3a60b4a3e8272036ed21f7863ed0d90d9e66c1fa5547ffadefccac250276da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.0766",
    "kind": "arxiv",
    "version": 3
  }
}