Pith Number

pith:GQLUUMVG

pith:2017:GQLUUMVGDVIKJX3ND4HBLHZOJW

not attested not anchored not stored refs pending

The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form $S^{2n+1}/ \Gamma$

Hui Liu

arxiv:1712.07000 v3 · 2017-12-18 · math.DS · math.DG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GQLUUMVGDVIKJX3ND4HBLHZOJW}

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	2026-05-17T23:44:38.348285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34174a32a61d50a4df6d1f0e159f2e4d8fbad383b76fdce703b7f10707f5dfdd

Aliases

arxiv: 1712.07000 · arxiv_version: 1712.07000v3 · doi: 10.48550/arxiv.1712.07000 · pith_short_12: GQLUUMVGDVIK · pith_short_16: GQLUUMVGDVIKJX3N · pith_short_8: GQLUUMVG

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/GQLUUMVGDVIKJX3ND4HBLHZOJW \
  | 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: 34174a32a61d50a4df6d1f0e159f2e4d8fbad383b76fdce703b7f10707f5dfdd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a17a7d3ec72f77f2736a06228be8827a110ac995b0d383fe8ae32cb082bd3842",
    "cross_cats_sorted": [
      "math.DG",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-12-18T08:16:19Z",
    "title_canon_sha256": "092f9aebbd22ad0ad4ab8cdd11670edb222f84b03b938897151d61c7b6b79f9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07000",
    "kind": "arxiv",
    "version": 3
  }
}