Pith Number

pith:M43FJXJV

pith:2004:M43FJXJV3LLWCKNJ3NJKO2BBMJ

not attested not anchored not stored refs pending

Backward volume contraction for endomorphisms with eventual volume expansion

Armando Castro, Jose F. Alves, Vilton Pinheiro

arxiv:math/0403537 v1 · 2004-03-31 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M43FJXJV3LLWCKNJ3NJKO2BBMJ}

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	2026-07-04T14:38:28.858298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

673654dd35dad76129a9db52a768216257dafa91443b1be54fba30378cabfc65

Aliases

arxiv: math/0403537 · arxiv_version: math/0403537v1 · doi: 10.48550/arxiv.math/0403537 · pith_short_12: M43FJXJV3LLW · pith_short_16: M43FJXJV3LLWCKNJ · pith_short_8: M43FJXJV

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/M43FJXJV3LLWCKNJ3NJKO2BBMJ \
  | 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: 673654dd35dad76129a9db52a768216257dafa91443b1be54fba30378cabfc65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5f5ccd7016738ae02f69d469c7f9adf17c3f4084467a8766253bbc1c5e1feda",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2004-03-31T10:30:59Z",
    "title_canon_sha256": "6f33c2d47abe4269785f309f07554c04d8085a1dcde6dcf4272914e2c5cd261b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0403537",
    "kind": "arxiv",
    "version": 1
  }
}