Pith Number

pith:JAMT3BWT

pith:2016:JAMT3BWTIOY6T3EFX7V5YQMOTO

not attested not anchored not stored refs pending

A simple proof of the closed graph theorem

A.G. Ramm

arxiv:1601.02600 v1 · 2016-01-09 · 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{JAMT3BWTIOY6T3EFX7V5YQMOTO}

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	2026-05-18T01:23:01.973226Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48193d86d343b1e9ec85bfebdc418e9b91c8d0b3d66705ff571e7ff89dc14b0b

Aliases

arxiv: 1601.02600 · arxiv_version: 1601.02600v1 · doi: 10.48550/arxiv.1601.02600 · pith_short_12: JAMT3BWTIOY6 · pith_short_16: JAMT3BWTIOY6T3EF · pith_short_8: JAMT3BWT

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/JAMT3BWTIOY6T3EFX7V5YQMOTO \
  | 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: 48193d86d343b1e9ec85bfebdc418e9b91c8d0b3d66705ff571e7ff89dc14b0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09df8e3c67228bec2a7a9b1e64bf19b443401938b74c27653da762ddeac71f69",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-01-09T00:41:08Z",
    "title_canon_sha256": "494a31c650a61fb9fa440046fc8fc8919d72963e7ca6018c34f9f2ce58c9cb1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.02600",
    "kind": "arxiv",
    "version": 1
  }
}