Pith Number

pith:RSODFQJG

pith:2018:RSODFQJGX5GBG4J5IMERKDCJU6

not attested not anchored not stored refs pending

The realization problem for discrete Morse functions on trees

Nicholas A. Scoville, Yuqing Liu

arxiv:1807.09149 v1 · 2018-07-24 · 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{RSODFQJGX5GBG4J5IMERKDCJU6}

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	2026-05-18T00:09:56.660068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c9c32c126bf4c13713d4309150c49a78b23c877aaaa07876d9234360ee016c5

Aliases

arxiv: 1807.09149 · arxiv_version: 1807.09149v1 · doi: 10.48550/arxiv.1807.09149 · pith_short_12: RSODFQJGX5GB · pith_short_16: RSODFQJGX5GBG4J5 · pith_short_8: RSODFQJG

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/RSODFQJGX5GBG4J5IMERKDCJU6 \
  | 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: 8c9c32c126bf4c13713d4309150c49a78b23c877aaaa07876d9234360ee016c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec61ff44045529e9591b7a7c0e4c2725f8619998539ba56fd3810153196e0b82",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2018-07-24T14:33:28Z",
    "title_canon_sha256": "dfd281665b1718cdbe969d8a26c73ea65fa54a5525f4673e25e2e0d4034ab3d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.09149",
    "kind": "arxiv",
    "version": 1
  }
}