Pith Number

pith:6JMHK5YC

pith:2009:6JMHK5YCA6QEYJQPVKM2D5ZN5R

not attested not anchored not stored refs pending

Symmetric topological complexity as the first obstruction in Goodwillie's Euclidean embedding tower for real projective spaces

Jesus Gonzalez

arxiv:0911.1116 v4 · 2009-11-05 · 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{6JMHK5YCA6QEYJQPVKM2D5ZN5R}

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	2026-05-18T04:41:44.872677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f25875770207a04c260faa99a1f72dec4df9f914d876b9f0393cf6c4e6bf0db7

Aliases

arxiv: 0911.1116 · arxiv_version: 0911.1116v4 · doi: 10.48550/arxiv.0911.1116 · pith_short_12: 6JMHK5YCA6QE · pith_short_16: 6JMHK5YCA6QEYJQP · pith_short_8: 6JMHK5YC

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/6JMHK5YCA6QEYJQPVKM2D5ZN5R \
  | 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: f25875770207a04c260faa99a1f72dec4df9f914d876b9f0393cf6c4e6bf0db7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f8155b7ece5bf627d70e342996ae6e454469c9d573b1645f1d140a95cf09e5b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-11-05T19:56:25Z",
    "title_canon_sha256": "9bf0c3672d18c0458ca9defb7f94fd5141a84c991ff1e007f865c662f4319623"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.1116",
    "kind": "arxiv",
    "version": 4
  }
}