Pith Number

pith:C6GI4YRF

pith:2012:C6GI4YRFMHLHMAM54BSUWHB5DV

not attested not anchored not stored refs pending

Univalence for inverse diagrams and homotopy canonicity

Michael Shulman

arxiv:1203.3253 v3 · 2012-03-15 · 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{C6GI4YRFMHLHMAM54BSUWHB5DV}

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	2026-05-17T23:53:18.852409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

178c8e622561d676019de0654b1c3d1d4ed0735ad062498ef2a8584085e01b54

Aliases

arxiv: 1203.3253 · arxiv_version: 1203.3253v3 · doi: 10.48550/arxiv.1203.3253 · pith_short_12: C6GI4YRFMHLH · pith_short_16: C6GI4YRFMHLHMAM5 · pith_short_8: C6GI4YRF

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/C6GI4YRFMHLHMAM54BSUWHB5DV \
  | 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: 178c8e622561d676019de0654b1c3d1d4ed0735ad062498ef2a8584085e01b54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b83c797fe43a08ce020ff8b947a4861506f3fd90e9c6fa6b4206b6222bfbb29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2012-03-15T02:17:29Z",
    "title_canon_sha256": "6460ecaa702a0e69996b65f3073161421ab31ddb0ff1a7106b489de06a07fe13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3253",
    "kind": "arxiv",
    "version": 3
  }
}