Pith Number

pith:AREXDXD7

pith:2014:AREXDXD7F6G5QMWQJMEZI3L5QK

not attested not anchored not stored refs pending

Optimal packing of spheres in $\mathbb R^d$ and extremal effective conductivity

Vladimir Mityushev

arxiv:1412.7527 v1 · 2014-12-23 · 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{AREXDXD7F6G5QMWQJMEZI3L5QK}

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	2026-05-18T02:30:33.597746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

044971dc7f2f8dd832d04b09946d7d82b12787556a2dd1f44bba30c019372bd0

Aliases

arxiv: 1412.7527 · arxiv_version: 1412.7527v1 · doi: 10.48550/arxiv.1412.7527 · pith_short_12: AREXDXD7F6G5 · pith_short_16: AREXDXD7F6G5QMWQ · pith_short_8: AREXDXD7

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/AREXDXD7F6G5QMWQJMEZI3L5QK \
  | 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: 044971dc7f2f8dd832d04b09946d7d82b12787556a2dd1f44bba30c019372bd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d64e2a44fbf9634b1a0fcf86ed3db987ad5442524bbb248766d259310953d907",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2014-12-23T10:32:30Z",
    "title_canon_sha256": "201d7f4956d38022209cac9b45d3f52c971aed46c7458dd861200886d50aa9fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.7527",
    "kind": "arxiv",
    "version": 1
  }
}