Pith Number

pith:ZC7IMSCO

pith:2016:ZC7IMSCOOD42WQRRKOUSXK7UIS

not attested not anchored not stored refs pending

Description and triviality of the loop products and coproducts for rational Gorenstein spaces

Shun Wakatsuki

arxiv:1612.03563 v1 · 2016-12-12 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZC7IMSCOOD42WQRRKOUSXK7UIS}

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	2026-05-18T00:55:18.946225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8be86484e70f9ab423153a92babf4448690d8ca7bf7f6bf04dab33867a143b7

Aliases

arxiv: 1612.03563 · arxiv_version: 1612.03563v1 · doi: 10.48550/arxiv.1612.03563 · pith_short_12: ZC7IMSCOOD42 · pith_short_16: ZC7IMSCOOD42WQRR · pith_short_8: ZC7IMSCO

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/ZC7IMSCOOD42WQRRKOUSXK7UIS \
  | 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: c8be86484e70f9ab423153a92babf4448690d8ca7bf7f6bf04dab33867a143b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4ecac36cb0f7823da8a4645e15d32688bed74484233d4f758c80851493acc63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-12-12T08:05:33Z",
    "title_canon_sha256": "1e293d7bbf4cceb17805262fceee105447824ed7ab7f4660fc96122dd204ef63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03563",
    "kind": "arxiv",
    "version": 1
  }
}