Pith Number

pith:WFFBTSMY

pith:2013:WFFBTSMYVYWTPMCVF6JHGGISIW

not attested not anchored not stored refs pending

Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots

Marianne Akian, Meisam Sharify, Stephane Gaubert

arxiv:1304.2967 v4 · 2013-04-10 · math.SP · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WFFBTSMYVYWTPMCVF6JHGGISIW}

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	2026-05-18T00:53:40.918170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b14a19c998ae2d37b0552f92731912459a95e1555df01496edf115cc8876f02c

Aliases

arxiv: 1304.2967 · arxiv_version: 1304.2967v4 · doi: 10.48550/arxiv.1304.2967 · pith_short_12: WFFBTSMYVYWT · pith_short_16: WFFBTSMYVYWTPMCV · pith_short_8: WFFBTSMY

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/WFFBTSMYVYWTPMCVF6JHGGISIW \
  | 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: b14a19c998ae2d37b0552f92731912459a95e1555df01496edf115cc8876f02c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e84469eca92d94580a904af033d9a4b921f936304319ce9d60f94f0abeb3c250",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-04-10T14:03:16Z",
    "title_canon_sha256": "5953ffa8913e5c53adee8b80f2b290a231d61cc5e74e8c39fcc95ddcf3866f4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.2967",
    "kind": "arxiv",
    "version": 4
  }
}