Pith Number

pith:MKQNB7FR

pith:2015:MKQNB7FR5U2R5I2CFTZNWSJ5B6

not attested not anchored not stored refs pending

Expansive maps are isometries

David A. Meyer, Orest Bucicovschi

arxiv:1507.05044 v1 · 2015-07-08 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MKQNB7FR5U2R5I2CFTZNWSJ5B6}

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	2026-05-18T01:36:42.047651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62a0d0fcb1ed351ea3422cf2db493d0f94987e1f637606efbadc4deda3c5d061

Aliases

arxiv: 1507.05044 · arxiv_version: 1507.05044v1 · doi: 10.48550/arxiv.1507.05044 · pith_short_12: MKQNB7FR5U2R · pith_short_16: MKQNB7FR5U2R5I2C · pith_short_8: MKQNB7FR

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/MKQNB7FR5U2R5I2CFTZNWSJ5B6 \
  | 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: 62a0d0fcb1ed351ea3422cf2db493d0f94987e1f637606efbadc4deda3c5d061

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edbb7f0406862fba4c5477ef1549370acbd04adb73d603622546ff001e658c85",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-07-08T02:41:39Z",
    "title_canon_sha256": "b6590dd7fcab75f443bf7757be2ebf70cbd4d9cf950d5fdace8e9240a3883231"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05044",
    "kind": "arxiv",
    "version": 1
  }
}