Pith Number

pith:LKZEKEL3

pith:2012:LKZEKEL3TNK6J4IUNBWSO2EFN2

not attested not anchored not stored refs pending

Martingales arising from minimal submanifolds and other geometric contexts

Robert W. Neel

arxiv:1210.4033 v4 · 2012-10-15 · math.DG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LKZEKEL3TNK6J4IUNBWSO2EFN2}

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	2026-05-18T01:22:58.154225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ab245117b9b55e4f114686d2768856eab11d825d065b06f0d3094715ac19359

Aliases

arxiv: 1210.4033 · arxiv_version: 1210.4033v4 · doi: 10.48550/arxiv.1210.4033 · pith_short_12: LKZEKEL3TNK6 · pith_short_16: LKZEKEL3TNK6J4IU · pith_short_8: LKZEKEL3

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/LKZEKEL3TNK6J4IUNBWSO2EFN2 \
  | 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: 5ab245117b9b55e4f114686d2768856eab11d825d065b06f0d3094715ac19359

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ab81554ca7f9b78a5a2a3184655cbf16eab3d370047f2982cfc2aaa579aa7c0",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-10-15T13:48:50Z",
    "title_canon_sha256": "231db68ea3a2aef02144309068d30e434a204f794ddd52870801d192db1c5e60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4033",
    "kind": "arxiv",
    "version": 4
  }
}