Pith Number

pith:AGGG36H6

pith:2013:AGGG36H6DCXIOBBXFXVSDQZTPP

not attested not anchored not stored refs pending

Morse theory for the Hofer length functional

Yasha Savelyev

arxiv:1308.3456 v3 · 2013-08-15 · math.SG · 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{AGGG36H6DCXIOBBXFXVSDQZTPP}

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	2026-05-18T02:53:53.668784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

018c6df8fe18ae8704372deb21c3337bf32c323307b210f6eb92e7cfac6081de

Aliases

arxiv: 1308.3456 · arxiv_version: 1308.3456v3 · doi: 10.48550/arxiv.1308.3456 · pith_short_12: AGGG36H6DCXI · pith_short_16: AGGG36H6DCXIOBBX · pith_short_8: AGGG36H6

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/AGGG36H6DCXIOBBXFXVSDQZTPP \
  | 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: 018c6df8fe18ae8704372deb21c3337bf32c323307b210f6eb92e7cfac6081de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4550aeae42392edaa47cab840888e99cb69fb11cff982a5586c918ad1457786",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-08-15T17:02:01Z",
    "title_canon_sha256": "a58483148ab9f130fd43b398c609fa3667013820592048192adcef66b50715be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3456",
    "kind": "arxiv",
    "version": 3
  }
}