{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:DWPQ4YPS23FXWY6J2LX6QZFGRC","short_pith_number":"pith:DWPQ4YPS","canonical_record":{"source":{"id":"math/0607641","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2006-07-25T19:43:08Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"96f02b8bb3256390b0ee3896378861ac0a0b43a14042204496602e104558a691","abstract_canon_sha256":"67060d0ae562bbf6dcc95be738afd3ebab52bdad42d5d60d5f89c91e3ae329d0"},"schema_version":"1.0"},"canonical_sha256":"1d9f0e61f2d6cb7b63c9d2efe864a6889b56a811464dc616c9ef3e9c4281cbce","source":{"kind":"arxiv","id":"math/0607641","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607641","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607641v1","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607641","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"DWPQ4YPS23FX","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"DWPQ4YPS23FXWY6J","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"DWPQ4YPS","created_at":"2026-06-03T22:06:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:DWPQ4YPS23FXWY6J2LX6QZFGRC","target":"record","payload":{"canonical_record":{"source":{"id":"math/0607641","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2006-07-25T19:43:08Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"96f02b8bb3256390b0ee3896378861ac0a0b43a14042204496602e104558a691","abstract_canon_sha256":"67060d0ae562bbf6dcc95be738afd3ebab52bdad42d5d60d5f89c91e3ae329d0"},"schema_version":"1.0"},"canonical_sha256":"1d9f0e61f2d6cb7b63c9d2efe864a6889b56a811464dc616c9ef3e9c4281cbce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:20.228637Z","signature_b64":"cDt6+QgryUE5A9ehyJUAblL02LInH9QWdLaMyQvPpbmO/AZmdeodPIo+PVruxEeQ8OA/O0G8GYFtZT2JgtTjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d9f0e61f2d6cb7b63c9d2efe864a6889b56a811464dc616c9ef3e9c4281cbce","last_reissued_at":"2026-06-03T22:06:20.228141Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:20.228141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0607641","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T22:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Me6OgNQWYevTPr5E7Cok7Czw6GYVqw1Ps1JvafNe7u/QSpDB1ZmmF3BLkJsasOBzSN8kwJDOWKZTwU0G9GJ7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:20:11.254497Z"},"content_sha256":"68db3f7c02cfbff9421f664a99ff55d2b4b2d955a3171d08664d514f7d363716","schema_version":"1.0","event_id":"sha256:68db3f7c02cfbff9421f664a99ff55d2b4b2d955a3171d08664d514f7d363716"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:DWPQ4YPS23FXWY6J2LX6QZFGRC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Non-Existence Result for Hamiltonian Integrators","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"P. F. Tupper","submitted_at":"2006-07-25T19:43:08Z","abstract_excerpt":"We consider the numerical simulation of Hamiltonian systems of ordinary differential equations. Two features of Hamiltonian systems are that energy is conserved along trajectories and phase space volume is preserved by the flow. We want to determine if there are integration schemes that preserve these two properties for all Hamiltonian systems, or at least for all systems in a wide class. This paper provides provides a negative result in the case of two dimensional (one degree of freedom) Hamiltonian systems, for which phase space volume is identical to area. Our main theorem shows that there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607641","kind":"arxiv","version":1},"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/math/0607641/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":"2026-06-03T22:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NdL5zXhDsx7LoZKxQj7i1WJDgxg7MQl3L0YDOwE5UHGX2oPeYir/WpLldX9na4/+R/5ImzYBsqARkZ60x0/wBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:20:11.254893Z"},"content_sha256":"40ac4cde8f7ff7d90f4a8c9ebcdb283805ad057486049cd068b3b5b4bdc1d4d6","schema_version":"1.0","event_id":"sha256:40ac4cde8f7ff7d90f4a8c9ebcdb283805ad057486049cd068b3b5b4bdc1d4d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWPQ4YPS23FXWY6J2LX6QZFGRC/bundle.json","state_url":"https://pith.science/pith/DWPQ4YPS23FXWY6J2LX6QZFGRC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWPQ4YPS23FXWY6J2LX6QZFGRC/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":"2026-06-08T13:20:11Z","links":{"resolver":"https://pith.science/pith/DWPQ4YPS23FXWY6J2LX6QZFGRC","bundle":"https://pith.science/pith/DWPQ4YPS23FXWY6J2LX6QZFGRC/bundle.json","state":"https://pith.science/pith/DWPQ4YPS23FXWY6J2LX6QZFGRC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWPQ4YPS23FXWY6J2LX6QZFGRC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DWPQ4YPS23FXWY6J2LX6QZFGRC","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":"67060d0ae562bbf6dcc95be738afd3ebab52bdad42d5d60d5f89c91e3ae329d0","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2006-07-25T19:43:08Z","title_canon_sha256":"96f02b8bb3256390b0ee3896378861ac0a0b43a14042204496602e104558a691"},"schema_version":"1.0","source":{"id":"math/0607641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607641","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607641v1","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607641","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"DWPQ4YPS23FX","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"DWPQ4YPS23FXWY6J","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"DWPQ4YPS","created_at":"2026-06-03T22:06:20Z"}],"graph_snapshots":[{"event_id":"sha256:40ac4cde8f7ff7d90f4a8c9ebcdb283805ad057486049cd068b3b5b4bdc1d4d6","target":"graph","created_at":"2026-06-03T22:06:20Z","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/math/0607641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the numerical simulation of Hamiltonian systems of ordinary differential equations. Two features of Hamiltonian systems are that energy is conserved along trajectories and phase space volume is preserved by the flow. We want to determine if there are integration schemes that preserve these two properties for all Hamiltonian systems, or at least for all systems in a wide class. This paper provides provides a negative result in the case of two dimensional (one degree of freedom) Hamiltonian systems, for which phase space volume is identical to area. Our main theorem shows that there ","authors_text":"P. F. Tupper","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2006-07-25T19:43:08Z","title":"A Non-Existence Result for Hamiltonian Integrators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607641","kind":"arxiv","version":1},"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":"sha256:68db3f7c02cfbff9421f664a99ff55d2b4b2d955a3171d08664d514f7d363716","target":"record","created_at":"2026-06-03T22:06:20Z","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":"67060d0ae562bbf6dcc95be738afd3ebab52bdad42d5d60d5f89c91e3ae329d0","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2006-07-25T19:43:08Z","title_canon_sha256":"96f02b8bb3256390b0ee3896378861ac0a0b43a14042204496602e104558a691"},"schema_version":"1.0","source":{"id":"math/0607641","kind":"arxiv","version":1}},"canonical_sha256":"1d9f0e61f2d6cb7b63c9d2efe864a6889b56a811464dc616c9ef3e9c4281cbce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d9f0e61f2d6cb7b63c9d2efe864a6889b56a811464dc616c9ef3e9c4281cbce","first_computed_at":"2026-06-03T22:06:20.228141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:20.228141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cDt6+QgryUE5A9ehyJUAblL02LInH9QWdLaMyQvPpbmO/AZmdeodPIo+PVruxEeQ8OA/O0G8GYFtZT2JgtTjAA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:20.228637Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68db3f7c02cfbff9421f664a99ff55d2b4b2d955a3171d08664d514f7d363716","sha256:40ac4cde8f7ff7d90f4a8c9ebcdb283805ad057486049cd068b3b5b4bdc1d4d6"],"state_sha256":"2db612e832da235d8c975df1bba10090a46f8551148dcd43633e30b31b34d6b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jHmepZZ9MdDfKcR1BbJ4Te0gcXrHLvT8hu4VZEEEymrEk/Pot4B68ygby+bbXxFOe766W3ydCU46Hg6YDvzJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:20:11.256872Z","bundle_sha256":"04120371408fe5cd883ffe6fc7f96b9ad9097fc2e092303a3d23f95122007c9b"}}