Pith Number

pith:NIIA2NQR

pith:2026:NIIA2NQRF2OHBSYHTIZSGOKAVN

not attested not anchored not stored refs resolved

On the Essence of Lagrange's Equations

Peng Shi

Lagrange's equations transform the kinetic energy theorem into the momentum theorem using the chain rule, showing how energy conservation builds momentum conservation.

arxiv:2605.15498 v1 · 2026-05-15 · physics.class-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NIIA2NQRF2OHBSYHTIZSGOKAVN}

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.

Claims

C1strongest claim

the essence of Lagrange's equations is identified as the transformation of the kinetic energy theorem into the momentum theorem via the chain rule for composite functions, thereby revealing how energy conservation constructs momentum conservation.

C2weakest assumption

That expressing the differential form of energy conservation in an arbitrary coordinate system and then performing suitable differential operations on it will directly produce Lagrange's equations (abstract, paragraph beginning 'Subsequently, expressing the differential form...').

C3one line summary

Lagrange's equations arise as the chain-rule transformation of the kinetic energy theorem into the momentum theorem, showing how energy conservation constructs momentum conservation.

References

10 extracted · 10 resolved · 0 Pith anchors

[1] P., and John S., Classical mechanics 1950

[2] N., and Janet D 1998

[3] Shastri S., Robotic Mechanical Systems Fundamentals. Educohack Press, 2025 2025

[4] H., Advanced engin eering dynamics 1998

[5] S., Classical continuum mechanics 2022

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:01.797667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a100d36112e9c70cb079a33233940ab6279a96ae0d6d7b98c0b3777da6d8c87

Aliases

arxiv: 2605.15498 · arxiv_version: 2605.15498v1 · doi: 10.48550/arxiv.2605.15498 · pith_short_12: NIIA2NQRF2OH · pith_short_16: NIIA2NQRF2OHBSYH · pith_short_8: NIIA2NQR

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/NIIA2NQRF2OHBSYHTIZSGOKAVN \
  | 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: 6a100d36112e9c70cb079a33233940ab6279a96ae0d6d7b98c0b3777da6d8c87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b440140d2630d336096d102600cdc4ec203b498442935ff65b71bb2ffb65c43b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "physics.class-ph",
    "submitted_at": "2026-05-15T00:32:12Z",
    "title_canon_sha256": "c23b200d14bbc603649acf30e932acde2412c88b9d83f7374908f6f7d3e2f464"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15498",
    "kind": "arxiv",
    "version": 1
  }
}