Pith Number

pith:3H344HOW

pith:2015:3H344HOWQ46EXPX4ZNNQXC5KFV

not attested not anchored not stored refs pending

Harmonic Measures on the Sphere via Curvature-Dimension

Emanuel Milman

arxiv:1505.04335 v1 · 2015-05-16 · math.MG · math.DG · math.FA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3H344HOWQ46EXPX4ZNNQXC5KFV}

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	2026-05-18T02:07:25.652909Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9f7ce1dd6873c4bbefccb5b0b8baa2d5271abae8c401b4e6fea40046188b7e1

Aliases

arxiv: 1505.04335 · arxiv_version: 1505.04335v1 · doi: 10.48550/arxiv.1505.04335 · pith_short_12: 3H344HOWQ46E · pith_short_16: 3H344HOWQ46EXPX4 · pith_short_8: 3H344HOW

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/3H344HOWQ46EXPX4ZNNQXC5KFV \
  | 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: d9f7ce1dd6873c4bbefccb5b0b8baa2d5271abae8c401b4e6fea40046188b7e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fdba31594504cd7f150d8ffb050af35983693407a4cec517be182ab3e2a1041",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-05-16T22:55:42Z",
    "title_canon_sha256": "2eb87b75bd1a2f6299ec65a993002c47010fdda3d1a0cd44ce0372082b05f825"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04335",
    "kind": "arxiv",
    "version": 1
  }
}