Pith Number

pith:FHWYUZNZ

pith:2016:FHWYUZNZCTPTZLTKTVUDB2UJS5

not attested not anchored not stored refs pending

The renormalization method based on the Taylor expansion and applications for asymptotic analysis

Cheng-shi Liu

arxiv:1605.02888 v1 · 2016-05-10 · math-ph · cond-mat.dis-nn · hep-th · math.CA · math.DS · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FHWYUZNZCTPTZLTKTVUDB2UJS5}

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	2026-05-18T01:15:08.291410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29ed8a65b914df3cae6a9d6830ea89976e6418e425edb6b7138227091e2d3bd7

Aliases

arxiv: 1605.02888 · arxiv_version: 1605.02888v1 · doi: 10.48550/arxiv.1605.02888 · pith_short_12: FHWYUZNZCTPT · pith_short_16: FHWYUZNZCTPTZLTK · pith_short_8: FHWYUZNZ

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/FHWYUZNZCTPTZLTKTVUDB2UJS5 \
  | 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: 29ed8a65b914df3cae6a9d6830ea89976e6418e425edb6b7138227091e2d3bd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdb9e8a85f27ce9a80e951ab4867e2bc4c4b490777b38507755daa50e32755ac",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "hep-th",
      "math.CA",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-05-10T08:20:21Z",
    "title_canon_sha256": "8f33797c4fa8216171276039faff17c8fa80ebfff1b0174a25578bb6b5dacd08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.02888",
    "kind": "arxiv",
    "version": 1
  }
}