Pith Number

pith:GGQT7GLH

pith:2012:GGQT7GLHXA4M7STQZ6OWRKBVO7

not attested not anchored not stored refs pending

Morse theory for Lagrange multipliers and adiabatic limits

Guangbo Xu, Stephen Schecter

arxiv:1211.3028 v3 · 2012-11-13 · math.GT · math.DS · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GGQT7GLHXA4M7STQZ6OWRKBVO7}

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	2026-05-18T02:39:55.842776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31a13f9967b838cfca70cf9d68a83577ee8bf6146783622e79296ea5d688ec6a

Aliases

arxiv: 1211.3028 · arxiv_version: 1211.3028v3 · doi: 10.48550/arxiv.1211.3028 · pith_short_12: GGQT7GLHXA4M · pith_short_16: GGQT7GLHXA4M7STQ · pith_short_8: GGQT7GLH

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/GGQT7GLHXA4M7STQZ6OWRKBVO7 \
  | 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: 31a13f9967b838cfca70cf9d68a83577ee8bf6146783622e79296ea5d688ec6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c85eb42df61c287c1a734fb07814c2301152f1a4c2c1c143b0d430a96856d15",
    "cross_cats_sorted": [
      "math.DS",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-11-13T15:54:08Z",
    "title_canon_sha256": "3ff97bb4a63eca3a5a2da17fdb867475bf687e00be0f2b7638b627e946fa2f22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3028",
    "kind": "arxiv",
    "version": 3
  }
}