Pith Number

pith:TWQ7O2CA

pith:2011:TWQ7O2CATG2F7KWEOEHBLOAAP2

not attested not anchored not stored refs pending

A model for the Whitehead product in rational mapping spaces

Takahito Naito

arxiv:1106.4080 v1 · 2011-06-21 · 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{TWQ7O2CATG2F7KWEOEHBLOAAP2}

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	2026-05-18T04:19:40.788096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9da1f7684099b45faac4710e15b8007eb92c7bfee319ef2a848491052d8d4ee1

Aliases

arxiv: 1106.4080 · arxiv_version: 1106.4080v1 · doi: 10.48550/arxiv.1106.4080 · pith_short_12: TWQ7O2CATG2F · pith_short_16: TWQ7O2CATG2F7KWE · pith_short_8: TWQ7O2CA

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/TWQ7O2CATG2F7KWEOEHBLOAAP2 \
  | 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: 9da1f7684099b45faac4710e15b8007eb92c7bfee319ef2a848491052d8d4ee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61da37e89eca287b650dd16a823584de266711bdff8e1b14349083dbe64e7cc9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-06-21T03:26:12Z",
    "title_canon_sha256": "3c23446b7df25f538284dc83b3060b936a4d3f5218f0fcabaf8e2d3d183a86ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4080",
    "kind": "arxiv",
    "version": 1
  }
}