Pith Number

pith:5ZUMGGYE

pith:2011:5ZUMGGYE5RFMYHD2DNLAGUEIRQ

not attested not anchored not stored refs pending

Circle-valued Morse theory for complex hyperplane arrangements

Andrei Pajitnov, Toshitake Kohno

arxiv:1101.0437 v2 · 2011-01-02 · 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{5ZUMGGYE5RFMYHD2DNLAGUEIRQ}

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	2026-05-18T04:06:19.115320Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee68c31b04ec4acc1c7a1b560350888c397705171e0e3375dbd9a46bd94429f1

Aliases

arxiv: 1101.0437 · arxiv_version: 1101.0437v2 · doi: 10.48550/arxiv.1101.0437 · pith_short_12: 5ZUMGGYE5RFM · pith_short_16: 5ZUMGGYE5RFMYHD2 · pith_short_8: 5ZUMGGYE

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/5ZUMGGYE5RFMYHD2DNLAGUEIRQ \
  | 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: ee68c31b04ec4acc1c7a1b560350888c397705171e0e3375dbd9a46bd94429f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d400972881d2630d042869c7835a509af944c7ead21ff074aafa8e084c3a9c0e",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-01-02T22:37:09Z",
    "title_canon_sha256": "86298ceb599f84c9f1852ba4d20425db989937617b6f69c873d5721342049bbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0437",
    "kind": "arxiv",
    "version": 2
  }
}