Pith Number

pith:LUESCRUM

pith:2015:LUESCRUMP5TLM3LK4WK52HOHAE

not attested not anchored not stored refs pending

Quotients and Hopf Images of a Smash Coproduct

Julien Bichon

arxiv:1507.00561 v1 · 2015-07-02 · math.QA · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LUESCRUMP5TLM3LK4WK52HOHAE}

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	2026-05-18T01:37:24.314856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d0921468c7f66b66d6ae595dd1dc701045778b3162198e42855ba20825956f0

Aliases

arxiv: 1507.00561 · arxiv_version: 1507.00561v1 · doi: 10.48550/arxiv.1507.00561 · pith_short_12: LUESCRUMP5TL · pith_short_16: LUESCRUMP5TLM3LK · pith_short_8: LUESCRUM

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/LUESCRUMP5TLM3LK4WK52HOHAE \
  | 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: 5d0921468c7f66b66d6ae595dd1dc701045778b3162198e42855ba20825956f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39fc2faf6931699211bf9b66c730db94c3c8f97c9f8e2bcb7e8ebc9374f46e2f",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-07-02T12:56:56Z",
    "title_canon_sha256": "62e147817050aa3b5c191dee9f7ebd2fc463aa93c3410826a94702bc2711f2e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.00561",
    "kind": "arxiv",
    "version": 1
  }
}