Pith Number

pith:YVENZ6TQ

pith:2013:YVENZ6TQ6LODNFI2HTMJEJKLZD

not attested not anchored not stored refs pending

Calculating the Fundamental Group of the Circle in Homotopy Type Theory

Daniel R. Licata, Michael Shulman

arxiv:1301.3443 v1 · 2013-01-15 · math.LO · cs.PL · 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{YVENZ6TQ6LODNFI2HTMJEJKLZD}

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	2026-05-18T03:36:25.593969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c548dcfa70f2dc36951a3cd892254bc8ec7bdf917672b92e301980519dba0bb4

Aliases

arxiv: 1301.3443 · arxiv_version: 1301.3443v1 · doi: 10.48550/arxiv.1301.3443 · pith_short_12: YVENZ6TQ6LOD · pith_short_16: YVENZ6TQ6LODNFI2 · pith_short_8: YVENZ6TQ

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/YVENZ6TQ6LODNFI2HTMJEJKLZD \
  | 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: c548dcfa70f2dc36951a3cd892254bc8ec7bdf917672b92e301980519dba0bb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3374cef6208c18214b0d16653c6e31fa95b824956f614441787d284a243a16f5",
    "cross_cats_sorted": [
      "cs.PL",
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2013-01-15T18:30:31Z",
    "title_canon_sha256": "65c53fa76ffb947eca3a9597b21432132cbfc43c2f6c3e11d9fdfe071c296bfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.3443",
    "kind": "arxiv",
    "version": 1
  }
}