Pith Number

pith:GZERH5DU

pith:2015:GZERH5DUWNSHAVE4WDR7UUGYGY

not attested not anchored not stored refs pending

Averaged projections, angles between groups and strengthening of property (T)

Izhar Oppenheim

arxiv:1507.08695 v4 · 2015-07-30 · math.GR · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GZERH5DUWNSHAVE4WDR7UUGYGY}

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	2026-05-18T00:52:23.896929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

364913f474b36470549cb0e3fa50d8361ed82e77a3a1123e89c72f7d8784240c

Aliases

arxiv: 1507.08695 · arxiv_version: 1507.08695v4 · doi: 10.48550/arxiv.1507.08695 · pith_short_12: GZERH5DUWNSH · pith_short_16: GZERH5DUWNSHAVE4 · pith_short_8: GZERH5DU

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/GZERH5DUWNSHAVE4WDR7UUGYGY \
  | 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: 364913f474b36470549cb0e3fa50d8361ed82e77a3a1123e89c72f7d8784240c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dc7bd084a42e1d2a6805aceb6109dbb580caab6952adee5ea19abc478289d81",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-07-30T21:32:30Z",
    "title_canon_sha256": "3ec6223ee038ecc6e9a52adcf1ef2c3667a431282b07057e33c63999883cb3e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08695",
    "kind": "arxiv",
    "version": 4
  }
}