Pith Number

pith:Q3KNW5PF

pith:2016:Q3KNW5PFNNRZOVDPJ4QAYNB2IJ

not attested not anchored not stored refs pending

Brouwer degree, domination of manifolds, and groups presentable by products

Pierre de la Harpe

arxiv:1609.06637 v1 · 2016-09-21 · 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{Q3KNW5PFNNRZOVDPJ4QAYNB2IJ}

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	2026-05-18T01:04:06.317365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86d4db75e56b6397546f4f200c343a426d2b06663d4281b88120505bc1363c4e

Aliases

arxiv: 1609.06637 · arxiv_version: 1609.06637v1 · doi: 10.48550/arxiv.1609.06637 · pith_short_12: Q3KNW5PFNNRZ · pith_short_16: Q3KNW5PFNNRZOVDP · pith_short_8: Q3KNW5PF

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/Q3KNW5PFNNRZOVDPJ4QAYNB2IJ \
  | 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: 86d4db75e56b6397546f4f200c343a426d2b06663d4281b88120505bc1363c4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62bf0fae67aa93c1935b4252eda04f187754ce772b5073146417b8d06dcfe5eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-09-21T17:00:40Z",
    "title_canon_sha256": "4e08b8553f6d2f09b176f1071a954feb9d25d5b43552d7006898f0a83b09c05e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06637",
    "kind": "arxiv",
    "version": 1
  }
}