Pith Number

pith:PZXZH33D

pith:2013:PZXZH33DC3IV3ET53XBP34ADNV

not attested not anchored not stored refs pending

New lower bounds for the topological complexity of aspherical spaces

Gregory Lupton, John Oprea, Mark Grant

arxiv:1309.4192 v1 · 2013-09-17 · 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{PZXZH33DC3IV3ET53XBP34ADNV}

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	2026-05-18T03:13:09.341916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e6f93ef6316d15d927dddc2fdf0036d7e6d62949e379616a18697b439176673

Aliases

arxiv: 1309.4192 · arxiv_version: 1309.4192v1 · doi: 10.48550/arxiv.1309.4192 · pith_short_12: PZXZH33DC3IV · pith_short_16: PZXZH33DC3IV3ET5 · pith_short_8: PZXZH33D

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/PZXZH33DC3IV3ET53XBP34ADNV \
  | 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: 7e6f93ef6316d15d927dddc2fdf0036d7e6d62949e379616a18697b439176673

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ea2e8040bc032f83300ae5b60700c65242afab9d730d9991d55278ff30dcd33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2013-09-17T06:12:26Z",
    "title_canon_sha256": "3a378e09264d2da82e0f8a6315475a59f15d7541a1d9d40d7155d93e40d485db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.4192",
    "kind": "arxiv",
    "version": 1
  }
}