Pith Number

pith:GGMPKJK4

pith:2013:GGMPKJK4WKKPVKKBPXFALVCPL2

not attested not anchored not stored refs pending

Index theory of the de Rham complex on manifolds with periodic ends

Daniel Ruberman, Nikolai Saveliev, Tomasz Mrowka

arxiv:1310.4246 v1 · 2013-10-16 · math.GT · 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{GGMPKJK4WKKPVKKBPXFALVCPL2}

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	2026-05-18T02:03:38.028992Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3198f5255cb294faa9417dca05d44f5ea229cf2ddbb7424ec453faa42e725773

Aliases

arxiv: 1310.4246 · arxiv_version: 1310.4246v1 · doi: 10.48550/arxiv.1310.4246 · pith_short_12: GGMPKJK4WKKP · pith_short_16: GGMPKJK4WKKPVKKB · pith_short_8: GGMPKJK4

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/GGMPKJK4WKKPVKKBPXFALVCPL2 \
  | 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: 3198f5255cb294faa9417dca05d44f5ea229cf2ddbb7424ec453faa42e725773

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3645866a19372838e1aa947f60d35f1e2e483b28821a2f6eb62f2fde59070727",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-10-16T02:16:52Z",
    "title_canon_sha256": "5c9f0bbf32da70b71cad73f7fe3501c6e5e9bc159ea999e44173ab55d9240c5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.4246",
    "kind": "arxiv",
    "version": 1
  }
}