Pith Number

pith:MM7RVIVO

pith:2012:MM7RVIVO5S7HBF2OF2BDXXQQZ4

not attested not anchored not stored refs pending

Lower bounds of principal eigenvalue in dimension one

Mu-Fa chen

arxiv:1206.5071 v1 · 2012-06-22 · math.PR · math.CA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MM7RVIVO5S7HBF2OF2BDXXQQZ4}

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	2026-05-18T03:52:52.433674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

633f1aa2aeecbe70974e2e823bde10cf0b422c7ce8e66ec832df93e2beaf2caa

Aliases

arxiv: 1206.5071 · arxiv_version: 1206.5071v1 · doi: 10.48550/arxiv.1206.5071 · pith_short_12: MM7RVIVO5S7H · pith_short_16: MM7RVIVO5S7HBF2O · pith_short_8: MM7RVIVO

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/MM7RVIVO5S7HBF2OF2BDXXQQZ4 \
  | 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: 633f1aa2aeecbe70974e2e823bde10cf0b422c7ce8e66ec832df93e2beaf2caa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "509945e3d6a5da983c98d069177ac61d407da4dacd5986c2f47fd19f4cf2fe7d",
    "cross_cats_sorted": [
      "math.CA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-22T07:13:10Z",
    "title_canon_sha256": "98f9e1c91b7bbe6972193df444c0628ad4b1907494fb34d03765bdda1037b067"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.5071",
    "kind": "arxiv",
    "version": 1
  }
}