Pith Number

pith:XF4NDFV5

pith:2014:XF4NDFV5YDPFKXGKIN4AWUT4MY

not attested not anchored not stored refs pending

The LS-category of the product of lens spaces

Alexander Dranishnikov

arxiv:1409.8316 v2 · 2014-09-29 · math.GT · 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{XF4NDFV5YDPFKXGKIN4AWUT4MY}

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	2026-05-18T01:22:21.714245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b978d196bdc0de555cca43780b527c6606ad08b36bf3d7ef3bd2d5c2eb1620fd

Aliases

arxiv: 1409.8316 · arxiv_version: 1409.8316v2 · doi: 10.48550/arxiv.1409.8316 · pith_short_12: XF4NDFV5YDPF · pith_short_16: XF4NDFV5YDPFKXGK · pith_short_8: XF4NDFV5

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/XF4NDFV5YDPFKXGKIN4AWUT4MY \
  | 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: b978d196bdc0de555cca43780b527c6606ad08b36bf3d7ef3bd2d5c2eb1620fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe9d178c7bf52f8c6eaaf85251520219823b805cc4fad2a0bd458ca4caa41fe0",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-09-29T20:39:41Z",
    "title_canon_sha256": "7c00b23b86b29a85bf4c135d2fc06e42991952f3bbc4696291922b1e8a7c5a6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.8316",
    "kind": "arxiv",
    "version": 2
  }
}