Pith Number

pith:BW72P4R4

pith:2016:BW72P4R4REGOF5EPWWWDQT43JL

not attested not anchored not stored refs pending

Sampling on the Sphere by Mutually Orthogonal Subspaces

Uri Grupel

arxiv:1607.03714 v2 · 2016-07-13 · 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{BW72P4R4REGOF5EPWWWDQT43JL}

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	2026-05-18T00:51:48.038127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0dbfa7f23c890ce2f48fb5ac384f9b4aef764e55233923caf7a6329b729c6b18

Aliases

arxiv: 1607.03714 · arxiv_version: 1607.03714v2 · doi: 10.48550/arxiv.1607.03714 · pith_short_12: BW72P4R4REGO · pith_short_16: BW72P4R4REGOF5EP · pith_short_8: BW72P4R4

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/BW72P4R4REGOF5EPWWWDQT43JL \
  | 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: 0dbfa7f23c890ce2f48fb5ac384f9b4aef764e55233923caf7a6329b729c6b18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f61ff7dc87d71446f2abe74536add7d80481c6f2da14de8388d128633f46a79",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-07-13T13:11:15Z",
    "title_canon_sha256": "b2d66af2795356ea0ed49e07f4f8b752e0ffa89e22d3153895fb08fb7cdaab6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.03714",
    "kind": "arxiv",
    "version": 2
  }
}