Pith Number

pith:4M5KBXSG

pith:2015:4M5KBXSGLINQJRKGN7BSHTWLBQ

not attested not anchored not stored refs pending

Spectral and Hodge theory of `Witt' incomplete cusp edge spaces

Jan Swoboda, Jesse Gell-Redman

arxiv:1509.06359 v1 · 2015-09-21 · math.AP · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4M5KBXSGLINQJRKGN7BSHTWLBQ}

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	2026-05-18T01:32:20.516640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e33aa0de465a1b04c5466fc323cecb0c3061bf98d1a3dd2aefe20468e9aac975

Aliases

arxiv: 1509.06359 · arxiv_version: 1509.06359v1 · doi: 10.48550/arxiv.1509.06359 · pith_short_12: 4M5KBXSGLINQ · pith_short_16: 4M5KBXSGLINQJRKG · pith_short_8: 4M5KBXSG

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/4M5KBXSGLINQJRKGN7BSHTWLBQ \
  | 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: e33aa0de465a1b04c5466fc323cecb0c3061bf98d1a3dd2aefe20468e9aac975

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdcd720c6dcbb027f17bea5c066851ad7ecd2cfc9f306377814440c489e311c9",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-21T19:44:23Z",
    "title_canon_sha256": "5f9ba4fa4954a4bf557bbecf732d2e05d377bf2947286dd550ca23313a8ff645"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06359",
    "kind": "arxiv",
    "version": 1
  }
}