Pith Number

pith:MRAM52MP

pith:2010:MRAM52MP23XOAR5BD5XYRJDJJ4

not attested not anchored not stored refs pending

The index quasi-periodicity and multiplicity of closed geodesics

Huagui Duan, Yiming Long

arxiv:1008.1458 v2 · 2010-08-09 · math.SG · math.DG · 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{MRAM52MP23XOAR5BD5XYRJDJJ4}

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	2026-05-18T04:41:55.659440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6440cee98fd6eee047a11f6f88a4694f2a129cb469e9e9b41332625b64954ae8

Aliases

arxiv: 1008.1458 · arxiv_version: 1008.1458v2 · doi: 10.48550/arxiv.1008.1458 · pith_short_12: MRAM52MP23XO · pith_short_16: MRAM52MP23XOAR5B · pith_short_8: MRAM52MP

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/MRAM52MP23XOAR5BD5XYRJDJJ4 \
  | 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: 6440cee98fd6eee047a11f6f88a4694f2a129cb469e9e9b41332625b64954ae8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa8bec601459dc86037e364ee3de38451aa42b6a43cc72897e207d477be530a1",
    "cross_cats_sorted": [
      "math.DG",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2010-08-09T06:52:51Z",
    "title_canon_sha256": "fa93709135112229157b22cbdb77390af8a4dc152c487a636ec8095eb57ac52f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1458",
    "kind": "arxiv",
    "version": 2
  }
}