Pith Number

pith:5VRRHAYC

pith:2011:5VRRHAYCHCVEHKY53CDVULNCPH

not attested not anchored not stored refs pending

Approximation of weak adjoints by reverse automatic differentiation of BDF methods

D\"orte Beigel, Hans Georg Bock, Leonard Wirsching, Mario S. Mommer

arxiv:1109.3061 v1 · 2011-09-14 · 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{5VRRHAYCHCVEHKY53CDVULNCPH}

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	2026-05-18T04:13:06.380153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed6313830238aa43ab1dd8875a2da279c72a4d674c2c24d5a92d66401f75fc09

Aliases

arxiv: 1109.3061 · arxiv_version: 1109.3061v1 · doi: 10.48550/arxiv.1109.3061 · pith_short_12: 5VRRHAYCHCVE · pith_short_16: 5VRRHAYCHCVEHKY5 · pith_short_8: 5VRRHAYC

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/5VRRHAYCHCVEHKY53CDVULNCPH \
  | 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: ed6313830238aa43ab1dd8875a2da279c72a4d674c2c24d5a92d66401f75fc09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec0948e7965b625c9de61817d190e17ee0b3652457593772f27baef6174565b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-09-14T12:35:11Z",
    "title_canon_sha256": "8c8caf20050c941274656608075c1e553de8b2aafefad8bc3312a610965f5518"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3061",
    "kind": "arxiv",
    "version": 1
  }
}