Pith Number

pith:4GKDSD4S

pith:2015:4GKDSD4SCHAILLV52YEO6SQDIG

not attested not anchored not stored refs pending

Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions

Yiming Long, Yuming Xiao

arxiv:1503.07006 v1 · 2015-03-24 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4GKDSD4SCHAILLV52YEO6SQDIG}

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	2026-05-18T02:20:29.556800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e194390f9211c085aebdd608ef4a03419ee09af975923a785edd0ab48716642d

Aliases

arxiv: 1503.07006 · arxiv_version: 1503.07006v1 · doi: 10.48550/arxiv.1503.07006 · pith_short_12: 4GKDSD4SCHAI · pith_short_16: 4GKDSD4SCHAILLV5 · pith_short_8: 4GKDSD4S

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/4GKDSD4SCHAILLV52YEO6SQDIG \
  | 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: e194390f9211c085aebdd608ef4a03419ee09af975923a785edd0ab48716642d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "562459989829d37218491b2cf79042dc4a54707e1eddddd30224ec2db513f100",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-03-24T12:22:37Z",
    "title_canon_sha256": "7a593e88ce3b54c58df82cd94c67d9a70463f233929c800e0053214f1bf439a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.07006",
    "kind": "arxiv",
    "version": 1
  }
}