{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:LUNXDODVS3WGUQBMNYCCBYOC7D","short_pith_number":"pith:LUNXDODV","canonical_record":{"source":{"id":"2208.09570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-20T00:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"d007296886097f34daa21558300da027d01cdc66e4c9ec55cba2d1cec7b64bf4","abstract_canon_sha256":"c851d64f94fda7fdd6f03b0bec5f974a07044792268aa25b54cd701e654c4076"},"schema_version":"1.0"},"canonical_sha256":"5d1b71b87596ec6a402c6e0420e1c2f8c2c1b025c1189494787730a0fd1356ca","source":{"kind":"arxiv","id":"2208.09570","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.09570","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"arxiv_version","alias_value":"2208.09570v2","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.09570","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"pith_short_12","alias_value":"LUNXDODVS3WG","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"pith_short_16","alias_value":"LUNXDODVS3WGUQBM","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"pith_short_8","alias_value":"LUNXDODV","created_at":"2026-07-05T05:21:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:LUNXDODVS3WGUQBMNYCCBYOC7D","target":"record","payload":{"canonical_record":{"source":{"id":"2208.09570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-20T00:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"d007296886097f34daa21558300da027d01cdc66e4c9ec55cba2d1cec7b64bf4","abstract_canon_sha256":"c851d64f94fda7fdd6f03b0bec5f974a07044792268aa25b54cd701e654c4076"},"schema_version":"1.0"},"canonical_sha256":"5d1b71b87596ec6a402c6e0420e1c2f8c2c1b025c1189494787730a0fd1356ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:21:54.054418Z","signature_b64":"863LpVOaYWjQNPwtJHisJ+Q5iLCj2NcNzVMpX6hIY66TAxUyc2ftOMNtxVrEFja9jmnmqUdJ8p7c0cJGSBIBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d1b71b87596ec6a402c6e0420e1c2f8c2c1b025c1189494787730a0fd1356ca","last_reissued_at":"2026-07-05T05:21:54.054000Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:21:54.054000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.09570","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:21:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zUP7P784S7TGRYoOgv4lyS/daSjUMTfT9VqSZhtyHxGWEh6L2edFxK31IYhV+RcKkk+MW+h31hTu829IqibgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T02:42:59.397596Z"},"content_sha256":"7d4d920c6ce200b13bfe607d0b8c5ad5a097515451d1dd8770530fdfc9f66dfb","schema_version":"1.0","event_id":"sha256:7d4d920c6ce200b13bfe607d0b8c5ad5a097515451d1dd8770530fdfc9f66dfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:LUNXDODVS3WGUQBMNYCCBYOC7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calculus on MDPs: Potential Shaping as a Gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Adam Gleave, Erik Jenner, Herke van Hoof","submitted_at":"2022-08-20T00:37:55Z","abstract_excerpt":"In reinforcement learning, different reward functions can be equivalent in terms of the optimal policies they induce. A particularly well-known and important example is potential shaping, a class of functions that can be added to any reward function without changing the optimal policy set under arbitrary transition dynamics. Potential shaping is conceptually similar to potentials, conservative vector fields and gauge transformations in math and physics, but this connection has not previously been formally explored. We develop a formalism for discrete calculus on graphs that abstract a Markov D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09570","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.09570/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:21:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NP8n9C+iG5gtNeZFiOm+hIM8VXynGK2Aj6dLtCzxBjW5EZsmYkX0PHnWTj2Tbmo//VoDFhj2QFOzo31OqtWODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T02:42:59.398363Z"},"content_sha256":"aaa0372afaec0efa1bb28698827032817bf62e680e266823280dea25ec417b3b","schema_version":"1.0","event_id":"sha256:aaa0372afaec0efa1bb28698827032817bf62e680e266823280dea25ec417b3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LUNXDODVS3WGUQBMNYCCBYOC7D/bundle.json","state_url":"https://pith.science/pith/LUNXDODVS3WGUQBMNYCCBYOC7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LUNXDODVS3WGUQBMNYCCBYOC7D/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-22T02:42:59Z","links":{"resolver":"https://pith.science/pith/LUNXDODVS3WGUQBMNYCCBYOC7D","bundle":"https://pith.science/pith/LUNXDODVS3WGUQBMNYCCBYOC7D/bundle.json","state":"https://pith.science/pith/LUNXDODVS3WGUQBMNYCCBYOC7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LUNXDODVS3WGUQBMNYCCBYOC7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:LUNXDODVS3WGUQBMNYCCBYOC7D","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c851d64f94fda7fdd6f03b0bec5f974a07044792268aa25b54cd701e654c4076","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-20T00:37:55Z","title_canon_sha256":"d007296886097f34daa21558300da027d01cdc66e4c9ec55cba2d1cec7b64bf4"},"schema_version":"1.0","source":{"id":"2208.09570","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.09570","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"arxiv_version","alias_value":"2208.09570v2","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.09570","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"pith_short_12","alias_value":"LUNXDODVS3WG","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"pith_short_16","alias_value":"LUNXDODVS3WGUQBM","created_at":"2026-07-05T05:21:54Z"},{"alias_kind":"pith_short_8","alias_value":"LUNXDODV","created_at":"2026-07-05T05:21:54Z"}],"graph_snapshots":[{"event_id":"sha256:aaa0372afaec0efa1bb28698827032817bf62e680e266823280dea25ec417b3b","target":"graph","created_at":"2026-07-05T05:21:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.09570/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In reinforcement learning, different reward functions can be equivalent in terms of the optimal policies they induce. A particularly well-known and important example is potential shaping, a class of functions that can be added to any reward function without changing the optimal policy set under arbitrary transition dynamics. Potential shaping is conceptually similar to potentials, conservative vector fields and gauge transformations in math and physics, but this connection has not previously been formally explored. We develop a formalism for discrete calculus on graphs that abstract a Markov D","authors_text":"Adam Gleave, Erik Jenner, Herke van Hoof","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-20T00:37:55Z","title":"Calculus on MDPs: Potential Shaping as a Gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.09570","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7d4d920c6ce200b13bfe607d0b8c5ad5a097515451d1dd8770530fdfc9f66dfb","target":"record","created_at":"2026-07-05T05:21:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c851d64f94fda7fdd6f03b0bec5f974a07044792268aa25b54cd701e654c4076","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-08-20T00:37:55Z","title_canon_sha256":"d007296886097f34daa21558300da027d01cdc66e4c9ec55cba2d1cec7b64bf4"},"schema_version":"1.0","source":{"id":"2208.09570","kind":"arxiv","version":2}},"canonical_sha256":"5d1b71b87596ec6a402c6e0420e1c2f8c2c1b025c1189494787730a0fd1356ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d1b71b87596ec6a402c6e0420e1c2f8c2c1b025c1189494787730a0fd1356ca","first_computed_at":"2026-07-05T05:21:54.054000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:21:54.054000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"863LpVOaYWjQNPwtJHisJ+Q5iLCj2NcNzVMpX6hIY66TAxUyc2ftOMNtxVrEFja9jmnmqUdJ8p7c0cJGSBIBDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:21:54.054418Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.09570","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d4d920c6ce200b13bfe607d0b8c5ad5a097515451d1dd8770530fdfc9f66dfb","sha256:aaa0372afaec0efa1bb28698827032817bf62e680e266823280dea25ec417b3b"],"state_sha256":"067e99b7887196ae2b76363cbd65590daa680634d0bf9a0883b255f5852961ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8fAIAYWjBA1VWjDOnlbuu2R8oQlAWyffEbo/E0GMPci/RNHO93PAhnTRhqV1INigCKCBX/npZjGEm0YDwd/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T02:42:59.403380Z","bundle_sha256":"275914c6d1e6cb794334ebc10ba3953b170aefb122d2073d54f566556d8a7545"}}