Pith Number

pith:YAVTNROR

pith:2019:YAVTNROREIFFSK6ZPROFWPWNWM

not attested not anchored not stored refs pending

Accurate Computation of the Log-Sum-Exp and Softmax Functions

Desmond J. Higham, Nicholas J. Higham, Pierre Blanchard

arxiv:1909.03469 v1 · 2019-09-08 · math.NA · cs.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{YAVTNROREIFFSK6ZPROFWPWNWM}

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	2026-07-05T00:03:05.963527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c02b36c5d1220a592bd97c5c5b3ecdb336a2b6a5140f99b82cba3735b0a28589

Aliases

arxiv: 1909.03469 · arxiv_version: 1909.03469v1 · doi: 10.48550/arxiv.1909.03469 · pith_short_12: YAVTNROREIFF · pith_short_16: YAVTNROREIFFSK6Z · pith_short_8: YAVTNROR

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/YAVTNROREIFFSK6ZPROFWPWNWM \
  | 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: c02b36c5d1220a592bd97c5c5b3ecdb336a2b6a5140f99b82cba3735b0a28589

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18eaf2c80a35c9cb1709a38850c3489fc38e181e8afacc92672048b1c732b0ba",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-09-08T13:45:57Z",
    "title_canon_sha256": "f82e4121cf091fea8221519d0aecb4ab13e7a7ed8d5946c67a5a9d78c7a11314"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.03469",
    "kind": "arxiv",
    "version": 1
  }
}