Pith Number

pith:4IW3LF4A

pith:2011:4IW3LF4AN43SUYGRD5A7GNFE5H

not attested not anchored not stored refs pending

Higher Whitehead torsion and the geometric assembly map

Wolfgang Steimle

arxiv:1105.2116 v2 · 2011-05-11 · math.KT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4IW3LF4AN43SUYGRD5A7GNFE5H}

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	2026-05-18T02:58:00.934571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e22db597806f372a60d11f41f334a4e9e6d51d69ac12ed1a4d8f894e476456e5

Aliases

arxiv: 1105.2116 · arxiv_version: 1105.2116v2 · doi: 10.48550/arxiv.1105.2116 · pith_short_12: 4IW3LF4AN43S · pith_short_16: 4IW3LF4AN43SUYGR · pith_short_8: 4IW3LF4A

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/4IW3LF4AN43SUYGRD5A7GNFE5H \
  | 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: e22db597806f372a60d11f41f334a4e9e6d51d69ac12ed1a4d8f894e476456e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66d9712ac760a29790a5500c7c50a2401dd394f27749658f4a1e014f39b44354",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2011-05-11T08:20:40Z",
    "title_canon_sha256": "1f6a563b184cd579c36360c575abc38d7e8a282ceff6ca4354a3df3e0288ea33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2116",
    "kind": "arxiv",
    "version": 2
  }
}