Pith Number

pith:QI4MHLLV

pith:2011:QI4MHLLV45BJAWDUYYU7DL5XQB

not attested not anchored not stored refs pending

Symplectic Harmonic theory and the Federer-Fleming deformation theorem

Yi Lin

arxiv:1112.2442 v3 · 2011-12-12 · 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{QI4MHLLV45BJAWDUYYU7DL5XQB}

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	2026-05-18T03:11:58.341177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8238c3ad75e742905874c629f1afb7806b40371ca23ff4f79d87fe75e949614d

Aliases

arxiv: 1112.2442 · arxiv_version: 1112.2442v3 · doi: 10.48550/arxiv.1112.2442 · pith_short_12: QI4MHLLV45BJ · pith_short_16: QI4MHLLV45BJAWDU · pith_short_8: QI4MHLLV

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/QI4MHLLV45BJAWDUYYU7DL5XQB \
  | 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: 8238c3ad75e742905874c629f1afb7806b40371ca23ff4f79d87fe75e949614d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2f438b48cebabd193cb75ef946b468015c953d74e90e6f69c5d6af8f1c715ba",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2011-12-12T05:01:38Z",
    "title_canon_sha256": "9d82ea4899ef85b63f0bc822957af04e7887eb4526f7522eacbb065673903113"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2442",
    "kind": "arxiv",
    "version": 3
  }
}