Pith Number

pith:YCNZQ5AU

pith:2015:YCNZQ5AUTG2WFNKBEML46VQCW5

not attested not anchored not stored refs pending

Presentably symmetric monoidal infinity-categories are represented by symmetric monoidal model categories

Steffen Sagave, Thomas Nikolaus

arxiv:1506.01475 v3 · 2015-06-04 · math.AT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YCNZQ5AUTG2WFNKBEML46VQCW5}

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	2026-05-18T00:34:00.331662Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c09b98741499b562b5412317cf5602b77adfb860b57f2e5b83cb84886980127c

Aliases

arxiv: 1506.01475 · arxiv_version: 1506.01475v3 · doi: 10.48550/arxiv.1506.01475 · pith_short_12: YCNZQ5AUTG2W · pith_short_16: YCNZQ5AUTG2WFNKB · pith_short_8: YCNZQ5AU

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/YCNZQ5AUTG2WFNKBEML46VQCW5 \
  | 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: c09b98741499b562b5412317cf5602b77adfb860b57f2e5b83cb84886980127c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13488457c354534c9f7576c9882c9779e4346e3cefea2647af95d75cf24b01e7",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-06-04T06:52:33Z",
    "title_canon_sha256": "dd239c9c18fae0f696c2e5afba035074b119840a3e331f75a8d0de62b040203f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.01475",
    "kind": "arxiv",
    "version": 3
  }
}