Pith Number

pith:SCHGJ5IU

pith:2008:SCHGJ5IUI45IBKFFUVMS5QE4CY

not attested not anchored not stored refs pending

An Alternative Definition of the Completion of Metric Spaces

Cheng Hao

arxiv:0810.0805 v3 · 2008-10-05 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SCHGJ5IUI45IBKFFUVMS5QE4CY}

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	2026-05-18T04:07:06.896732Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

908e64f514473a80a8a5a5592ec09c1616bbaf5e1bc5061c492e9e56a739daae

Aliases

arxiv: 0810.0805 · arxiv_version: 0810.0805v3 · doi: 10.48550/arxiv.0810.0805 · pith_short_12: SCHGJ5IUI45I · pith_short_16: SCHGJ5IUI45IBKFF · pith_short_8: SCHGJ5IU

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/SCHGJ5IUI45IBKFFUVMS5QE4CY \
  | 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: 908e64f514473a80a8a5a5592ec09c1616bbaf5e1bc5061c492e9e56a739daae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a57563c054478bc17e16068ec80a5549c1b9a005b6edc96c85a749a9f8b762a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2008-10-05T06:21:24Z",
    "title_canon_sha256": "f90aa52a8446cf1d3c5079ea6f210b66831237123350d5e7099c1a1f779dc971"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.0805",
    "kind": "arxiv",
    "version": 3
  }
}