Pith Number

pith:W4FVVWPT

pith:2018:W4FVVWPTKKYNVZQGTUQI35KJYR

not attested not anchored not stored refs pending

The Whitehead exact sequence and the classification problem of homotopy types

Mahmoud Benkhalifa

arxiv:1802.09867 v4 · 2018-02-27 · 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{W4FVVWPTKKYNVZQGTUQI35KJYR}

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	2026-05-18T00:17:53.373874Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b70b5ad9f352b0dae6069d208df549c4633239ffbf36318c078430d5a17ba798

Aliases

arxiv: 1802.09867 · arxiv_version: 1802.09867v4 · doi: 10.48550/arxiv.1802.09867 · pith_short_12: W4FVVWPTKKYN · pith_short_16: W4FVVWPTKKYNVZQG · pith_short_8: W4FVVWPT

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/W4FVVWPTKKYNVZQGTUQI35KJYR \
  | 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: b70b5ad9f352b0dae6069d208df549c4633239ffbf36318c078430d5a17ba798

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbc86e8316e3e36ab8fad4003bc1d8a8704fa70f9fa5cb25832f5567dd99042b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2018-02-27T13:21:22Z",
    "title_canon_sha256": "fb85f04c5d2dec08388150e6a04ff981dbae0fbb49cbb7ba22e09558af3088a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.09867",
    "kind": "arxiv",
    "version": 4
  }
}