Pith Number

pith:LH5KAB2J

pith:2013:LH5KAB2J4JS7KAWNA6OBENGXEL

not attested not anchored not stored refs pending

The quantitative Morse theorem

Phan Phien, Ta Le Loi

arxiv:1305.3352 v1 · 2013-05-15 · math.NA · 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{LH5KAB2J4JS7KAWNA6OBENGXEL}

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	2026-05-18T03:25:36.068814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59faa00749e265f502cd079c1234d722fbb5438f03c65740d81e68eddb3dd29e

Aliases

arxiv: 1305.3352 · arxiv_version: 1305.3352v1 · doi: 10.48550/arxiv.1305.3352 · pith_short_12: LH5KAB2J4JS7 · pith_short_16: LH5KAB2J4JS7KAWN · pith_short_8: LH5KAB2J

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/LH5KAB2J4JS7KAWNA6OBENGXEL \
  | 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: 59faa00749e265f502cd079c1234d722fbb5438f03c65740d81e68eddb3dd29e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be70bdac8f16f430f537f547ae48920744519955594f0a5ab44a945ce19ed40a",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-05-15T04:46:21Z",
    "title_canon_sha256": "4a732dba170b782f3c11d8f0ae4a8c1ea5f9e95b890ccda6a99ada19dfa20a40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.3352",
    "kind": "arxiv",
    "version": 1
  }
}