Pith Number

pith:ZNU62SDB

pith:2015:ZNU62SDBXMQCSA4SFWR6YUFUAJ

not attested not anchored not stored refs pending

A refinement of Betti numbers in the presence of a continuous function. ( I )

Dan Burghelea

arxiv:1501.01012 v5 · 2015-01-05 · 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{ZNU62SDBXMQCSA4SFWR6YUFUAJ}

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	2026-05-18T00:21:00.661427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb69ed4861bb202903922da3ec50b402770e962720c060d973892aa6a6dabaf0

Aliases

arxiv: 1501.01012 · arxiv_version: 1501.01012v5 · doi: 10.48550/arxiv.1501.01012 · pith_short_12: ZNU62SDBXMQC · pith_short_16: ZNU62SDBXMQCSA4S · pith_short_8: ZNU62SDB

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/ZNU62SDBXMQCSA4SFWR6YUFUAJ \
  | 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: cb69ed4861bb202903922da3ec50b402770e962720c060d973892aa6a6dabaf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "459804237cbf7ac9da893366ce5c2e2de6aa4d38dbe8f277b9f20777da83f487",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-01-05T21:25:05Z",
    "title_canon_sha256": "7784b1ca478d2476a9e88e363c055cec8399a8969059fa18e5083b858bb191ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.01012",
    "kind": "arxiv",
    "version": 5
  }
}