Pith Number

pith:VVRCHBMF

pith:2010:VVRCHBMFOP2W5DOEJAS7IHB6EQ

not attested not anchored not stored refs pending

Discrete Morse Theory Is At Least As Perfect As Morse Theory

Bruno Benedetti

arxiv:1010.0548 v5 · 2010-10-04 · math.DG · math.AT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VVRCHBMFOP2W5DOEJAS7IHB6EQ}

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	2026-05-18T02:48:02.538189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad6223858573f56e8dc44825f41c3e241d4d3101158ba7166cb96e5fa8974175

Aliases

arxiv: 1010.0548 · arxiv_version: 1010.0548v5 · doi: 10.48550/arxiv.1010.0548 · pith_short_12: VVRCHBMFOP2W · pith_short_16: VVRCHBMFOP2W5DOE · pith_short_8: VVRCHBMF

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/VVRCHBMFOP2W5DOEJAS7IHB6EQ \
  | 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: ad6223858573f56e8dc44825f41c3e241d4d3101158ba7166cb96e5fa8974175

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c5d9d3a8755966bf4665648267eb2ea3f71525fabde5e9e8cbc337fd1fe49b1",
    "cross_cats_sorted": [
      "math.AT",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-10-04T11:37:10Z",
    "title_canon_sha256": "3be56c1998cd10ee556ad810d2b19483e75af81d3e0d7dc39316d00e8ea61bd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0548",
    "kind": "arxiv",
    "version": 5
  }
}