{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JIEP72C6C3BPQP3CWY3LNVGPE5","short_pith_number":"pith:JIEP72C6","canonical_record":{"source":{"id":"1207.0654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-07-03T12:39:06Z","cross_cats_sorted":[],"title_canon_sha256":"b817b20f44657bd07d2cf6e93cd1f33f597d39a0b6c2dc25630f43d86387d892","abstract_canon_sha256":"0abf524a26a89b6863f0d43df4e9c59cf3f902429e4c36cd297cf09a9a912495"},"schema_version":"1.0"},"canonical_sha256":"4a08ffe85e16c2f83f62b636b6d4cf2755e4c5c449ba10e3cd1e2b28693985bc","source":{"kind":"arxiv","id":"1207.0654","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0654","created_at":"2026-05-18T03:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0654v1","created_at":"2026-05-18T03:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0654","created_at":"2026-05-18T03:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"JIEP72C6C3BP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JIEP72C6C3BPQP3C","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JIEP72C6","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JIEP72C6C3BPQP3CWY3LNVGPE5","target":"record","payload":{"canonical_record":{"source":{"id":"1207.0654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-07-03T12:39:06Z","cross_cats_sorted":[],"title_canon_sha256":"b817b20f44657bd07d2cf6e93cd1f33f597d39a0b6c2dc25630f43d86387d892","abstract_canon_sha256":"0abf524a26a89b6863f0d43df4e9c59cf3f902429e4c36cd297cf09a9a912495"},"schema_version":"1.0"},"canonical_sha256":"4a08ffe85e16c2f83f62b636b6d4cf2755e4c5c449ba10e3cd1e2b28693985bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:57.543938Z","signature_b64":"UG6GEARHoom5q7dEi1GD1jXpF1j5L9WIunIYfW7pZ7Czx6EOhH2VzXSfTCysqbgZc7bBBBT3BmRRuoBypCzlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a08ffe85e16c2f83f62b636b6d4cf2755e4c5c449ba10e3cd1e2b28693985bc","last_reissued_at":"2026-05-18T03:51:57.543223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:57.543223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.0654","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":"2026-05-18T03:51:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NKSY9dN35ZY+5XpXRFOUnWAZp1h/UhUXZgeGC3FqQDauW1LEv2qDVejbirrCoat8jX672b7kDjEybRtuFKSpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:38:53.188368Z"},"content_sha256":"39f42918bf9ac45c3e3a466e4e6b84051b52cd9a1048779df0fe4facd2213e1f","schema_version":"1.0","event_id":"sha256:39f42918bf9ac45c3e3a466e4e6b84051b52cd9a1048779df0fe4facd2213e1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JIEP72C6C3BPQP3CWY3LNVGPE5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the set of Fixed Points of the Parallel Symmetric Sand Pile Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Kevin Perrot, Thi Ha Duong Phan, Trung Van Pham","submitted_at":"2012-07-03T12:39:06Z","abstract_excerpt":"Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of Self-Organized Criticality. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Usin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0654","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":""},"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":"2026-05-18T03:51:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"03EiaXCYS5lQR3nL4/VjIEbjzWc/26PwxX4vWm9T54pcv6+aj63Scfqycyes0fp8AWLQzx2QD5zTByJFd72NAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:38:53.188727Z"},"content_sha256":"1584e55202405111a8b6d3cff5c6c4ce30a41bc29eaa34a41acf830b2f755880","schema_version":"1.0","event_id":"sha256:1584e55202405111a8b6d3cff5c6c4ce30a41bc29eaa34a41acf830b2f755880"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIEP72C6C3BPQP3CWY3LNVGPE5/bundle.json","state_url":"https://pith.science/pith/JIEP72C6C3BPQP3CWY3LNVGPE5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIEP72C6C3BPQP3CWY3LNVGPE5/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":"2026-05-26T11:38:53Z","links":{"resolver":"https://pith.science/pith/JIEP72C6C3BPQP3CWY3LNVGPE5","bundle":"https://pith.science/pith/JIEP72C6C3BPQP3CWY3LNVGPE5/bundle.json","state":"https://pith.science/pith/JIEP72C6C3BPQP3CWY3LNVGPE5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIEP72C6C3BPQP3CWY3LNVGPE5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JIEP72C6C3BPQP3CWY3LNVGPE5","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":"0abf524a26a89b6863f0d43df4e9c59cf3f902429e4c36cd297cf09a9a912495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-07-03T12:39:06Z","title_canon_sha256":"b817b20f44657bd07d2cf6e93cd1f33f597d39a0b6c2dc25630f43d86387d892"},"schema_version":"1.0","source":{"id":"1207.0654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0654","created_at":"2026-05-18T03:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0654v1","created_at":"2026-05-18T03:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0654","created_at":"2026-05-18T03:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"JIEP72C6C3BP","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JIEP72C6C3BPQP3C","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JIEP72C6","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:1584e55202405111a8b6d3cff5c6c4ce30a41bc29eaa34a41acf830b2f755880","target":"graph","created_at":"2026-05-18T03:51:57Z","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"},"paper":{"abstract_excerpt":"Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of Self-Organized Criticality. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Usin","authors_text":"Kevin Perrot, Thi Ha Duong Phan, Trung Van Pham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-07-03T12:39:06Z","title":"On the set of Fixed Points of the Parallel Symmetric Sand Pile Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0654","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":"sha256:39f42918bf9ac45c3e3a466e4e6b84051b52cd9a1048779df0fe4facd2213e1f","target":"record","created_at":"2026-05-18T03:51:57Z","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":"0abf524a26a89b6863f0d43df4e9c59cf3f902429e4c36cd297cf09a9a912495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-07-03T12:39:06Z","title_canon_sha256":"b817b20f44657bd07d2cf6e93cd1f33f597d39a0b6c2dc25630f43d86387d892"},"schema_version":"1.0","source":{"id":"1207.0654","kind":"arxiv","version":1}},"canonical_sha256":"4a08ffe85e16c2f83f62b636b6d4cf2755e4c5c449ba10e3cd1e2b28693985bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a08ffe85e16c2f83f62b636b6d4cf2755e4c5c449ba10e3cd1e2b28693985bc","first_computed_at":"2026-05-18T03:51:57.543223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:57.543223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UG6GEARHoom5q7dEi1GD1jXpF1j5L9WIunIYfW7pZ7Czx6EOhH2VzXSfTCysqbgZc7bBBBT3BmRRuoBypCzlDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:57.543938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39f42918bf9ac45c3e3a466e4e6b84051b52cd9a1048779df0fe4facd2213e1f","sha256:1584e55202405111a8b6d3cff5c6c4ce30a41bc29eaa34a41acf830b2f755880"],"state_sha256":"556ccb72dbf13276bcbc4a5edd29c37015b8be70738c5f0664cf023a6cc36c0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BoPCr5GGYHqZ5CCpryHpN8FElplXmUx3UbCME+8sd2c3RB1aS15nghL/uuZOKXA2yiXb/1n/Wwrvc0p3IUz/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:38:53.191634Z","bundle_sha256":"6509c356d632c10568cca599dafc253e3830bcaa2dc7a74fe942e19a891a9f5b"}}