Pith Number

pith:4TNPQMGB

pith:2009:4TNPQMGBFPGQKBQU7TMHTMJO7B

not attested not anchored not stored refs pending

The geometry of modified Riemannian extensions

E. Calvino-Louzao, E. Garcia-Rio, P. Gilkey, R. Vazquez-Lorenzo

arxiv:0901.1633 v1 · 2009-01-12 · 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{4TNPQMGBFPGQKBQU7TMHTMJO7B}

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	2026-05-18T02:15:02.552052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4daf830c12bcd050614fcd879b12ef86dce4186ed80620b0b880c8a9384fb27

Aliases

arxiv: 0901.1633 · arxiv_version: 0901.1633v1 · doi: 10.48550/arxiv.0901.1633 · pith_short_12: 4TNPQMGBFPGQ · pith_short_16: 4TNPQMGBFPGQKBQU · pith_short_8: 4TNPQMGB

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/4TNPQMGBFPGQKBQU7TMHTMJO7B \
  | 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: e4daf830c12bcd050614fcd879b12ef86dce4186ed80620b0b880c8a9384fb27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "593b89de6fdf10188758a4b2c13ce9615719e95a0ef1f79098b8c2592f8703e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-01-12T18:32:51Z",
    "title_canon_sha256": "10a06d3bbaa8ec458fa8904f6b3578024da327cc2668c56a29e8aeeccc8b3cc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.1633",
    "kind": "arxiv",
    "version": 1
  }
}