Pith Number

pith:KQZO56UO

pith:2011:KQZO56UOMLMTLTM4VPROCIY7BC

not attested not anchored not stored refs pending

Lower bounds for topological complexity

Aleksandra Franc, Petar Pave\v{s}i\'c

arxiv:1110.6876 v4 · 2011-10-31 · 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{KQZO56UOMLMTLTM4VPROCIY7BC}

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	2026-05-18T03:27:33.057895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5432eefa8e62d935cd9cabe2e1231f089f43d778d1759938f08c02763e7efb61

Aliases

arxiv: 1110.6876 · arxiv_version: 1110.6876v4 · doi: 10.48550/arxiv.1110.6876 · pith_short_12: KQZO56UOMLMT · pith_short_16: KQZO56UOMLMTLTM4 · pith_short_8: KQZO56UO

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/KQZO56UOMLMTLTM4VPROCIY7BC \
  | 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: 5432eefa8e62d935cd9cabe2e1231f089f43d778d1759938f08c02763e7efb61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3aaf9b7cd60feac122be3623dd0dcd19745f49e1e7939a3f75caf441d613492f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-10-31T18:06:03Z",
    "title_canon_sha256": "f77ae9bd49c4f8fe14b16899a8e11e2032b757059ce9ff8bd8f1cf08b32d02a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6876",
    "kind": "arxiv",
    "version": 4
  }
}