Pith Number

pith:WEGMVO36

pith:2013:WEGMVO36F7KL4V64GAKDDXXJZR

not attested not anchored not stored refs pending

The Third Homotopy Group as a pi_1-Module

Beatrice Bleile, Hans-Joachim Baues

arxiv:1309.6510 v1 · 2013-09-25 · 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{WEGMVO36F7KL4V64GAKDDXXJZR}

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	2026-05-18T03:12:20.810068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b10ccabb7e2fd4be57dc301431dee9cc5243865a875c6222b90877ffde3deab1

Aliases

arxiv: 1309.6510 · arxiv_version: 1309.6510v1 · doi: 10.48550/arxiv.1309.6510 · pith_short_12: WEGMVO36F7KL · pith_short_16: WEGMVO36F7KL4V64 · pith_short_8: WEGMVO36

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/WEGMVO36F7KL4V64GAKDDXXJZR \
  | 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: b10ccabb7e2fd4be57dc301431dee9cc5243865a875c6222b90877ffde3deab1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afa0a9f485eab02f6338120202a4c8c5f5afa8f31596c19f014a61537c942002",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2013-09-25T14:05:55Z",
    "title_canon_sha256": "abe1752d24e9f7bb5c72b715d4ceadf1192ecc96d3597cd8b1dc4a0cf22332e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6510",
    "kind": "arxiv",
    "version": 1
  }
}