Pith Number

pith:QZ7WE2YO

pith:2009:QZ7WE2YOXMS7IMTRNFDMKU4MX7

not attested not anchored not stored refs pending

Topological Complexity and non-immersions of real projective space

Mark Grant

arxiv:0912.1212 v2 · 2009-12-07 · 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{QZ7WE2YOXMS7IMTRNFDMKU4MX7}

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	2026-05-18T04:24:27.749165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

867f626b0ebb25f432716946c5538cbff1f683c7407cce26d3f643e1d7f339c4

Aliases

arxiv: 0912.1212 · arxiv_version: 0912.1212v2 · doi: 10.48550/arxiv.0912.1212 · pith_short_12: QZ7WE2YOXMS7 · pith_short_16: QZ7WE2YOXMS7IMTR · pith_short_8: QZ7WE2YO

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/QZ7WE2YOXMS7IMTRNFDMKU4MX7 \
  | 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: 867f626b0ebb25f432716946c5538cbff1f683c7407cce26d3f643e1d7f339c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d31fee9d89d1647367427a715c6039f4fe60a2a4dc925a7b40636724c20e59c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-12-07T12:11:41Z",
    "title_canon_sha256": "93352308dbd5251cddbecf739efd40312a4eb8c938b04abdf27ddf8ac689708d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1212",
    "kind": "arxiv",
    "version": 2
  }
}