Pith Number

pith:APG33D4S

pith:2020:APG33D4SOANJ65KGLMYGSZ4HGC

not attested not anchored not stored refs pending

Spaces of embeddings: Nonsingular bilinear maps, chirality, and their generalizations

Florian Frick, Michael Harrison

arxiv:2010.11996 v1 · 2020-10-22 · math.GT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{APG33D4SOANJ65KGLMYGSZ4HGC}

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	2026-07-05T01:45:32.463429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03cdbd8f92701a9f75465b3069678730bb0e3f1a95492ece21a52c8ab1235cef

Aliases

arxiv: 2010.11996 · arxiv_version: 2010.11996v1 · doi: 10.48550/arxiv.2010.11996 · pith_short_12: APG33D4SOANJ · pith_short_16: APG33D4SOANJ65KG · pith_short_8: APG33D4S

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/APG33D4SOANJ65KGLMYGSZ4HGC \
  | 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: 03cdbd8f92701a9f75465b3069678730bb0e3f1a95492ece21a52c8ab1235cef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb47ac583305be700d1aed3dfaf2372f5a79e34591f458b82d07981c3732f2c7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2020-10-22T19:16:34Z",
    "title_canon_sha256": "1dbd5ed9c31aef5e898aaebe12781c7c10bb33bbf2bcf1a1b7a710261ca5c5ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.11996",
    "kind": "arxiv",
    "version": 1
  }
}