Pith Number

pith:SP5C3DM7

pith:2015:SP5C3DM7ABIQ5WSK3NWWMFX4HU

not attested not anchored not stored refs pending

On Cheeger and Sobolev differentials in metric measure spaces

Martin Kell

arxiv:1512.00828 v1 · 2015-12-02 · math.MG · 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{SP5C3DM7ABIQ5WSK3NWWMFX4HU}

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	2026-05-18T01:25:25.013289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93fa2d8d9f00510eda4adb6d6616fc3d33da4ee748c9a6823b0b695262fd43d9

Aliases

arxiv: 1512.00828 · arxiv_version: 1512.00828v1 · doi: 10.48550/arxiv.1512.00828 · pith_short_12: SP5C3DM7ABIQ · pith_short_16: SP5C3DM7ABIQ5WSK · pith_short_8: SP5C3DM7

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/SP5C3DM7ABIQ5WSK3NWWMFX4HU \
  | 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: 93fa2d8d9f00510eda4adb6d6616fc3d33da4ee748c9a6823b0b695262fd43d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c11f768ea1cba4713c5f8987b2eef389f49619cb099588f8b2e13733a025858",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-12-02T20:13:13Z",
    "title_canon_sha256": "09027b4248993111fc17ddbd4bbae1686ec5db5f4f4925ee24cd685a1780e06c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00828",
    "kind": "arxiv",
    "version": 1
  }
}