Pith Number

pith:SFOKXGQB

pith:2015:SFOKXGQBBI2IAPTONY4ILSWBCR

not attested not anchored not stored refs pending

An invariant of fiberwise Morse functions on surface bundle over $S^1$ by counting graphs

Tadayuki Watanabe

arxiv:1503.08735 v2 · 2015-03-30 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SFOKXGQBBI2IAPTONY4ILSWBCR}

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	2026-05-18T02:16:40.782579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

915cab9a010a34803e6e6e3885cac1146bbe12e664e45e9e07adaab86f049a4f

Aliases

arxiv: 1503.08735 · arxiv_version: 1503.08735v2 · doi: 10.48550/arxiv.1503.08735 · pith_short_12: SFOKXGQBBI2I · pith_short_16: SFOKXGQBBI2IAPTO · pith_short_8: SFOKXGQB

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/SFOKXGQBBI2IAPTONY4ILSWBCR \
  | 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: 915cab9a010a34803e6e6e3885cac1146bbe12e664e45e9e07adaab86f049a4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "714edb7acc0e568c1b7cc5dcb5a9737f91615ddeda26f6d06542eb56fcc9d12e",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-03-30T16:28:53Z",
    "title_canon_sha256": "3dcf4edc6e7a16f7d6dfc1066450ade6288ce05a323ac280b7d318be403ff575"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08735",
    "kind": "arxiv",
    "version": 2
  }
}