Enßlin & Weig (2010)
Inference with minimal Gibbs free energy in information field theory.
Design-rationale lineage only; it does not define the exact HydraDG G* equation.
HydraDG · linked terminology + custody
Project-specific terms are navigation objects, not decorative labels. Each declared term resolves to a definition, a deterministic website Knowledge FCO, a graph query, and an upstream source/receipt when one exists. The canonical project FCG has a hosted HydraDB readback receipt; website term FCOs remain an application metadata projection rather than a separate correctness claim.
Context scorer contract
| Quantity | Declared contract |
|---|---|
| shannon | H = -Σ p log2(p) |
| normalized shannon | Hnorm = H / log2(n) |
| g star | G* = U* - 0.35 × Hnorm |
| delta g star | ΔG*(t) = G*(t) - G*(t-1) |
| cloud drift | Cloud Drift = 100 × JSD_base2(Pt || P_reference) |
| mutation distance | Mutation distance = total-variation distance from the reference distribution |
| restoration gain | Restoration gain = max(0, previous TV distance - current TV distance) |
G* / ΔG* are application-defined dimensionless diagnostics. Enßlin & Weig (2010) is design-rationale lineage for the information/free-energy analogy; HydraDG's exact formula is defined by the checked scorer above. Lin (1991) is the source lineage for Jensen-Shannon divergence / Cloud Drift.
Academic foundations
Inference with minimal Gibbs free energy in information field theory.
Design-rationale lineage only; it does not define the exact HydraDG G* equation.
Divergence measures based on the Shannon entropy.
Jensen-Shannon divergence source lineage for Cloud Drift = 100 × JSD.
Fractal Custody Object: a content-addressed logical custody object with explicit evidence and claim boundaries.
How to: Inspect an FCO ID, its single canonical object SHA-256, payload, evidence class, claim ceiling, and source/dependency edges rather than treating a hash as truth.
knowledge_fco=fco:63031d39a118f3fee64c3834db9997c724ea86a696c8a9e11040daabb65e7f10
object_sha256=63031d39a118f3fee64c3834db9997c724ea86a696c8a9e11040daabb65e7f10
graph_query=FCO
Fractal Custody Graph: the dependency and transformation graph connecting sources, evidence, derived state, claims, and artifacts.
How to: Follow the canonical project relationship vocabulary to locate the source and transformation route behind a result; do not infer correctness merely because a path exists.
knowledge_fco=fco:78fe5323bd6ba1b1a7d0e36180ff86cf1152a44c35c3e3d783da72aa90d89bbc
object_sha256=78fe5323bd6ba1b1a7d0e36180ff86cf1152a44c35c3e3d783da72aa90d89bbc
graph_query=DERIVED_FROM
03
Governed source/evidence intake layer used to preserve content identity, provenance, and structured atomization before downstream projection.
How to: Use SeedGraph through its governed intake/ledger surface and preserve exact-source identity before downstream transforms.
knowledge_fco=fco:7e6e233a1c2f533b3eb9af61ff66b33b76e9621cdc4af2a3ff66eefdb092872d
object_sha256=7e6e233a1c2f533b3eb9af61ff66b33b76e9621cdc4af2a3ff66eefdb092872d
graph_query=SeedGraph
04
A bounded context-bearing evidence fragment produced from an exact source span or deterministic transform.
How to: Open the source/evidence node first, then follow its derivation into the atom; do not collapse source bytes and semantic interpretation into one identity.
knowledge_fco=fco:e7b75364b6ba51c11947057d12d96fada44309bf0d5d8d41a1e40656d3ea1f7e
object_sha256=e7b75364b6ba51c11947057d12d96fada44309bf0d5d8d41a1e40656d3ea1f7e
graph_query=KnowledgeAtom
05
A bounded admitted proposition supported by explicit atoms/evidence; not an absolute-truth label.
How to: Follow support dependencies back to admitted atoms and inspect the claim ceiling before reusing the seed.
knowledge_fco=fco:3ef3e40d84440693677cc4784794c40650e765a42525d1d9293bafc010b4fb51
object_sha256=3ef3e40d84440693677cc4784794c40650e765a42525d1d9293bafc010b4fb51
graph_query=SeedOfTruth
Mechanical Scientific Method: executable observation → hypothesis → experiment → measurement → comparison/falsification → update.
How to: Use declared controls and perturbations so the next experiment is a mechanically inspectable state transition and preserve null/negative outcomes.
knowledge_fco=fco:edba2f10ead9255ca2a776abcaf4309e9c622df8c98e282ddf6adda155c5e6ea
object_sha256=edba2f10ead9255ca2a776abcaf4309e9c622df8c98e282ddf6adda155c5e6ea
graph_query=StateSnapshot
07
Independent SELF/NONSELF × SAFE/NONSAFE + UNKNOWN admission/classification surface.
How to: Treat classification as a scoped event. It may admit, challenge, quarantine, abstain, or reject without overwriting provenance.
knowledge_fco=fco:994abc0e6927470000e22eae1d7a4a6f280eda0e0225670f9ed7eb0e22528090
object_sha256=994abc0e6927470000e22eae1d7a4a6f280eda0e0225670f9ed7eb0e22528090
graph_query=ClassificationReceipt
08
Temporal edge preserving an older authentic state while pointing toward a later state.
How to: Traverse the declared current-state chain rather than deleting the predecessor; the historical state remains part of custody.
knowledge_fco=fco:ee88b6fb9adc2d3cc224a7e29f059fc5252607902aa2364f7cd3dae8f8e1844a
object_sha256=ee88b6fb9adc2d3cc224a7e29f059fc5252607902aa2364f7cd3dae8f8e1844a
graph_query=SUPERSEDED_BY
09
Explicit relation between incompatible values or claims retained simultaneously in the graph.
How to: Use contradiction as a retrieval/reasoning signal and preserve both sides with their source/provenance context.
knowledge_fco=fco:6a546f3d6a5bb64370458f688e186ab1cb32a054262e0f03f2a997008290b956
object_sha256=6a546f3d6a5bb64370458f688e186ab1cb32a054262e0f03f2a997008290b956
graph_query=CONTRADICTS
10
The state selected by the declared temporal/supersession rules at a specific evaluation time, not an erasure of prior states.
How to: Resolve current state from the relevant state-transition path and preserve the predecessor, contradiction, and source chain.
knowledge_fco=fco:4fc3fb9b9dafbd9dd0c6934b6015ac68246e777630781ef7732a05993701f2e5
object_sha256=4fc3fb9b9dafbd9dd0c6934b6015ac68246e777630781ef7732a05993701f2e5
graph_query=current_state
11
A declared intervention that changes a load-bearing input, value, edge, configuration, or state for a falsification test.
How to: Record the target, before/after state, operator, scope, expected effect, and FCG delta. A perturbation is not automatically poison or unsafe.
knowledge_fco=fco:96417c0db002e84e99ae63067f9663607220ebbbc36e0aecb69fe8c1d54a35a4
object_sha256=96417c0db002e84e99ae63067f9663607220ebbbc36e0aecb69fe8c1d54a35a4
graph_query=Perturbation
12
A declared recovery intervention intended to restore a reference-compatible state without deleting perturbation history.
How to: Apply restoration as a new state, then compare the current-state and outcome metrics against the frozen reference while retaining the poison path.
knowledge_fco=fco:dac354d92fe2f156cd751df875f6d25431acbddf0b0c3013903fda00d029cd76
object_sha256=dac354d92fe2f156cd751df875f6d25431acbddf0b0c3013903fda00d029cd76
graph_query=restoration
13
HydraDG presentation model that places ΔG* and Cloud Drift at the visible tip while retaining the full FCO/FCG, provenance, statistical and receipt decomposition below the waterline.
How to: Treat the hero as a read-only projection. Rotate x/y/z, scrub time, inspect node halos, then follow the selected FCO into its custody route rather than treating the visualization as the evidence source.
knowledge_fco=fco:6ae3f5b4d2cb879048be066852699420422fd542c8e4a05b5234706b699bfa41
object_sha256=6ae3f5b4d2cb879048be066852699420422fd542c8e4a05b5234706b699bfa41
graph_query=StateSnapshot
14
Bounded context-distribution drift magnitude defined in v1 as 100 × Jensen-Shannon divergence from a frozen reference distribution.
How to: Use halo width/size to visualize magnitude only. Do not interpret a larger or smaller cloud as better accuracy; compare hit/recall and the preregistered nulls separately.
knowledge_fco=fco:2b60bce138cf35e15a6b2780e57449681eca66283610a090a9718ccbbd733369
object_sha256=2b60bce138cf35e15a6b2780e57449681eca66283610a090a9718ccbbd733369
graph_query=cloud_drift_0_100
15
Symmetric bounded divergence between two probability distributions; HydraDG uses base-2 logs so the v1 value lies in [0,1] before scaling to Cloud Drift 0–100.
How to: Verify the reference distribution, bucket vocabulary and scorer/config roots were frozen before comparing states. Source lineage: Lin (1991), Divergence measures based on the Shannon entropy.
knowledge_fco=fco:7fa58bb310fedd8a90a5214d9127fca7acc5d596f1dae4e105b3d28028d8c409
object_sha256=7fa58bb310fedd8a90a5214d9127fca7acc5d596f1dae4e105b3d28028d8c409
graph_query=js_divergence
16
Shannon entropy H = -∑ p log₂ p: information-state uncertainty / distribution breadth across the declared state distribution.
How to: HydraDG also uses Hnorm = H / log₂(n) in the synthetic G* scorer. Source lineage: Shannon (1948), A Mathematical Theory of Communication.
knowledge_fco=fco:6dce815c214c19579a610493d1b04e91da72ab1b30824b533bb419d350de6d03
object_sha256=6dce815c214c19579a610493d1b04e91da72ab1b30824b533bb419d350de6d03
graph_query=StateSnapshot
HydraDG synthetic-fixture scalar: G* = U* - 0.35 × Hnorm, where U* is the declared burden input and Hnorm is normalized Shannon entropy.
How to: Treat G* as an application-defined dimensionless information-state diagnostic. Enßlin & Weig (2010) is design-rationale lineage for the information/free-energy analogy; it does not define HydraDG's exact formula. No physical Gibbs-energy units are claimed.
knowledge_fco=fco:92f319f1b3229895d587f6b4fb1b1f856104dd3fbb2624ce07821bd75686b56b
object_sha256=92f319f1b3229895d587f6b4fb1b1f856104dd3fbb2624ce07821bd75686b56b
graph_query=StateSnapshot
Signed stepwise change in the HydraDG synthetic-fixture scalar: ΔG*(t) = G*(t) - G*(t-1).
How to: Interpret sign/direction only within the declared scorer contract. ΔG* is not physical Gibbs free energy and is not an accuracy score; Lin (1991) applies to JSD/Cloud Drift, not to this ΔG* formula.
knowledge_fco=fco:17443bb87fa0d7f0304387d6e7c534a201e751dcf5f8f9241b3a4212d058a4d9
object_sha256=17443bb87fa0d7f0304387d6e7c534a201e751dcf5f8f9241b3a4212d058a4d9
graph_query=delta_g_star
19
Synthetic-fixture mutation distance is total-variation distance between the frozen reference distribution and the current distribution.
How to: Keep this lane separate from Cloud Drift/JSD. In the checked scorer, total-variation distance is 0.5 × Σ|p_ref - p_t| after normalization.
knowledge_fco=fco:f0d40a084e8d4dfa98e1f50aa328e004d5467824af25247a34317854c5266d8e
object_sha256=f0d40a084e8d4dfa98e1f50aa328e004d5467824af25247a34317854c5266d8e
graph_query=mutation_distance
20
Synthetic-fixture restoration gain = max(0, previous total-variation distance - current total-variation distance).
How to: A positive value means movement back toward the frozen reference in the declared TV-distance lane. It is not ΔJSD and does not erase the poison state.
knowledge_fco=fco:c423544fb6a03abea6304f58742bf67d8e90eb5ebf803097208e4af9172de2fb
object_sha256=c423544fb6a03abea6304f58742bf67d8e90eb5ebf803097208e4af9172de2fb
graph_query=restoration_gain
21
Declared normalized burden input U* ∈ [0,1] used by the synthetic G* fixture contract.
How to: For the current fixture, U* is explicitly supplied for each state; do not claim it was inferred from contradiction-edge density unless a separate governed scorer and receipt establishes that mapping.
knowledge_fco=fco:67d7eb8f8cb9d49dd2eac9f7330255169b21fec8c5e583598046032be9d637ec
object_sha256=67d7eb8f8cb9d49dd2eac9f7330255169b21fec8c5e583598046032be9d637ec
graph_query=burden
22
Explicit classification of how evidence was obtained, such as directly supplied, externally retrieved, recomputed, deterministic transform, probabilistic model output, or inference.
How to: Keep evidence class attached to the object/result so downstream claims cannot silently promote a model output into a measured finding.
knowledge_fco=fco:2d6264ee14e215979d85a937bfdc9d323a5891424d7d4a19d7cf286d9a8d467f
object_sha256=2d6264ee14e215979d85a937bfdc9d323a5891424d7d4a19d7cf286d9a8d467f
graph_query=evidence_class
23
Maximum assertion strength supported by the current load-bearing evidence dependencies.
How to: A hash, replay, model output, or signature can only promote the specific property it actually establishes.
knowledge_fco=fco:f81b0bdca0c26b03161230758ec61f6e79dacbfb547c2cfe7a7e8635180937af
object_sha256=f81b0bdca0c26b03161230758ec61f6e79dacbfb547c2cfe7a7e8635180937af
graph_query=claim_ceiling
24
Deterministic commitment over a declared ordered leaf set; distinct from signing, correctness, and live HydraDB graph state.
How to: Inspect leaf ordering, odd-leaf rule, root SHA-256, and exact scope before describing a checkpoint as committed.
knowledge_fco=fco:9f7320fa4e7decb810e91f7726baedc73088f6dfdf2e5e1ee18e899e83fdf472
object_sha256=9f7320fa4e7decb810e91f7726baedc73088f6dfdf2e5e1ee18e899e83fdf472
graph_query=MerkleCheckpoint
Operational graph/context substrate used by HydraDG for typed state, relations, traversal, retrieval, connector-backed context and hosted projection/readback.
How to: Use the pinned/local lane for reproducibility and the hosted hydradg database for separately evidenced production readback; canonical FCO SHA-256 identity remains backend-independent.
knowledge_fco=fco:1bd50750c2a6b73f55779f77325dae25308f52ed93318b778ae02e6a8967dd8c
object_sha256=1bd50750c2a6b73f55779f77325dae25308f52ed93318b778ae02e6a8967dd8c
graph_query=HydraDB
26
Primary public Track 03 memory benchmark used by the completed full500 run.
How to: Use answer_session_ids for evaluation only; never graph construction or ranking.
knowledge_fco=fco:ff894ecb2967e9bf0ee69e0e9c348a0a684ce97b50f1fd8fa523e9746dd6178a
object_sha256=ff894ecb2967e9bf0ee69e0e9c348a0a684ce97b50f1fd8fa523e9746dd6178a
graph_query=LongMemEval
27
Primary Track 01 synthetic enterprise retrieval/reasoning corpus.
How to: Model source artifacts, entities, conflicting/stale claims, current state, and evidence paths; keep benchmark data evaluation-only.
knowledge_fco=fco:950142db44c8063d40a9983b3823473611a1ad991c439d6ef4dc3204bb631f3c
object_sha256=950142db44c8063d40a9983b3823473611a1ad991c439d6ef4dc3204bb631f3c
graph_query=EnterpriseRAG-Bench
Heterogeneous enterprise deep-search benchmark used as the Track 01 stress dataset.
How to: Use as a private/local evaluation source unless the intended public use passes the CC-BY-NC-4.0 release-license review.
knowledge_fco=fco:8f5e36ea184ff852eed61453948081a9d9b33fecf04693e9a0e8ec31c31c7938
object_sha256=8f5e36ea184ff852eed61453948081a9d9b33fecf04693e9a0e8ec31c31c7938
graph_query=HERB
29
Track 03 environment-experience memory benchmark with trajectories, haystacks, and optional screenshots.
How to: Start with released question/trajectory/haystack objects; pull screenshot archives only when the visual evidence lane is needed.
knowledge_fco=fco:760165c3f7d08e40b9e0a980ed1d43723284f8fbdb64c8031c5e1baaef27c992
object_sha256=760165c3f7d08e40b9e0a980ed1d43723284f8fbdb64c8031c5e1baaef27c992
graph_query=LongMemEval-V2
Long-context memory benchmark across 100K/500K/1M and separately 10M-token-scale conversations.
How to: Keep probing questions/ideal answers evaluation-only and ingest conversation turns as the memory substrate.
knowledge_fco=fco:31b87dcb8787709c0fcc4f805899bb4dcf09310f0b1c14305569abb5746a3a6a
object_sha256=31b87dcb8787709c0fcc4f805899bb4dcf09310f0b1c14305569abb5746a3a6a
graph_query=BEAM
31
Track 01 HydraDG experiment for enterprise context, identity resolution, conflicting evidence, and ontology state.
How to: Use bounded entity-resolution canaries first; only promote to real benchmark claims after the corresponding EnterpriseRAG/HERB receipts exist.
knowledge_fco=fco:da497052c6158548663924c4358481e292cb527719b65873803cb6cde57a4c22
object_sha256=da497052c6158548663924c4358481e292cb527719b65873803cb6cde57a4c22
graph_query=HydraOntology
32
Track 02A HydraDG experiment for dependency blast radius and poison → partial repair → full repair traversal.
How to: Compare HydraDB reverse dependency traversal against an independent deterministic closure before using real package/advisory evidence.
knowledge_fco=fco:3ff94610b84e6545cd7dadd43c7d619f35709dfca46efab3348f82d5aed4f8e6
object_sha256=3ff94610b84e6545cd7dadd43c7d619f35709dfca46efab3348f82d5aed4f8e6
graph_query=HydraBlast
33
Track 03 HydraDG experiment for longitudinal memory, supersession, contradiction, retrieval, and recovery.
How to: Preserve the completed null/negative full500 retrieval result while separately executing fresh state-transition golden paths and future governed treatment comparisons.
knowledge_fco=fco:b9ee524e8438b608c01f3efd147a1412f90a5ec3c8ee6123c93921b05d8ff432
object_sha256=b9ee524e8438b608c01f3efd147a1412f90a5ec3c8ee6123c93921b05d8ff432
graph_query=HydraMemory
34
Content-addressed submission hero media FCO with sponsor/track annotation regions for Immersive Commons judge navigation.
How to: Open /submission, inspect the SubmissionHeroMediaFCO by hash, and follow golden-path steps without treating the image as canonical FCG append evidence.
knowledge_fco=fco:47aa0f3a9f4313043fe93f0ce6512436f164c3772a54b7669910a5b23802b850
object_sha256=47aa0f3a9f4313043fe93f0ce6512436f164c3772a54b7669910a5b23802b850
graph_query=SubmissionHeroMediaFCO
35
HydraDG software is Apache-2.0; FCO/FCG research content and designated submission media are CC BY-NC-ND 4.0.
How to: Read LICENSING.md before reusing artifacts. License metadata is rights declaration only — not a hash, signature, or scientific verification result.
knowledge_fco=fco:7a3a6448b05c7c26429894b8ee722e351f8828a9465153578b82ee0d0c1e2bbf
object_sha256=7a3a6448b05c7c26429894b8ee722e351f8828a9465153578b82ee0d0c1e2bbf
graph_query=license
Each website FCO has one canonical SHA-256 identity. External academic links are source references; the internal Knowledge FCO is the website's custody-resolved navigation object. A digest or graph path does not establish scientific correctness by itself.