Pith Number

pith:B5QMLLDD

pith:1999:B5QMLLDDHVDO6JAD5RYAY356RV

not attested not anchored not stored refs pending

On Loops Representing Elements of the Fundamental Group of a Complete Manifold with Nonnegative Ricci Curvature

Christina Sormani

arxiv:math/9904096 v1 · 1999-04-19 · 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{B5QMLLDDHVDO6JAD5RYAY356RV}

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	2026-07-04T14:49:26.497790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f60c5ac633d46ef2403ec700c6fbe8d51338e35d8358cd0c2d699db5f3c6c45

Aliases

arxiv: math/9904096 · arxiv_version: math/9904096v1 · doi: 10.48550/arxiv.math/9904096 · pith_short_12: B5QMLLDDHVDO · pith_short_16: B5QMLLDDHVDO6JAD · pith_short_8: B5QMLLDD

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/B5QMLLDDHVDO6JAD5RYAY356RV \
  | 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: 0f60c5ac633d46ef2403ec700c6fbe8d51338e35d8358cd0c2d699db5f3c6c45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b42e6393ca312f0812b19f2b593d1ef35cfc4d6106cdbc13318272208710bde9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "1999-04-19T17:12:06Z",
    "title_canon_sha256": "cc464ee71c90748fbc7db8a4626bd4fb6198772e9a928e1bca66076748ae4b90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9904096",
    "kind": "arxiv",
    "version": 1
  }
}