Pith Number

pith:XOABG3U2

pith:2015:XOABG3U2NVQOJYRXM5U5UL6VE3

not attested not anchored not stored refs pending

Relations Between partial Metric Spaces and M-Metric Spaces, Caristi Kirk's Theorem in $M-$Metric Type Spaces

K. Abodayeh, N. Mlaiki, T. Abdeljawad, W.Shatanawi

arxiv:1512.06611 v1 · 2015-12-21 · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XOABG3U2NVQOJYRXM5U5UL6VE3}

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	2026-05-18T01:04:28.242561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb80136e9a6d60e4e2376769da2fd526e57438e94cd090e5db24d589c9fbe633

Aliases

arxiv: 1512.06611 · arxiv_version: 1512.06611v1 · doi: 10.48550/arxiv.1512.06611 · pith_short_12: XOABG3U2NVQO · pith_short_16: XOABG3U2NVQOJYRX · pith_short_8: XOABG3U2

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/XOABG3U2NVQOJYRXM5U5UL6VE3 \
  | 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: bb80136e9a6d60e4e2376769da2fd526e57438e94cd090e5db24d589c9fbe633

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "062f7fec57201e4c0008b7b4dec825fe4135e2d9318fc4eabcbb7a16263a5b95",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2015-12-21T13:06:18Z",
    "title_canon_sha256": "95e957457b4f5ec362eaaad71cbcd0c8c0bf74e79d1e108be4e103c40e65e115"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06611",
    "kind": "arxiv",
    "version": 1
  }
}